The first 498 Bernoulli Numbers;

Title: Editor: The first 498 Bernoulli Numbers Simon Plouffe [Etext #2586] April, 2001 *The Project Gutenberg Etext of The first 498 Bernoulli Numbers* ******This file should be named brnll10.txt or brnll10.zip****** Corrected EDITIONS of our etexts get a new NUMBER, brnll11.txt VERSIONS based on separate sources get new LETTER, brnll10a.txt Mathematical constants and numbers edited by Simon Plouffe Associate Professor LaCIM, University of Quebec at Montreal http://www.lacim.uqam.ca/pi : Plouffe's Inverter plouffe@math.uqam.ca Project Gutenberg Etexts are usually created from multiple editions, all of which are in the Public Domain in the United States, unless a copyright notice is included. Therefore, we usually do NOT keep any of these books in compliance with any particular paper edition. We are now trying to release all our books one month in advance of the official release dates, leaving time for better editing. 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We are planning on making some changes in our donation structure in 2000, so you might want to email me, hart@pobox.com beforehand. *END THE SMALL PRINT! FOR PUBLIC DOMAIN ETEXTS*Ver.04.29.93*END* Mathematical constants and numbers edited by Simon Plouffe Associate Professor LaCIM, University of Quebec at Montreal http://www.lacim.uqam.ca/pi : Plouffe's Inverter plouffe@math.uqam.ca The first 498 Bernoulli numbers are the coefficients of the series expansion of t*exp(x*t)/(exp(t)-1) = sum( B(n,x)/n!*t^n, n=0..infinity ). Bernoulli(2) 1/6 Bernoulli(4) -1/30 Bernoulli(6) 1/42 Bernoulli(8) -1/30 Bernoulli(10) 5/66 Bernoulli(12) -691/2730 Bernoulli(14) 7/6 Bernoulli(16) -3617/510 Bernoulli(18) 43867/798 Bernoulli(20) -174611/330 Bernoulli(22) 854513/138 Bernoulli(24) -236364091/2730 Bernoulli(26) 8553103/6 Bernoulli(28) -23749461029/870 Bernoulli(30) 8615841276005/14322 Bernoulli(32) -7709321041217/510 Bernoulli(34) 2577687858367/6 Bernoulli(36) -26315271553053477373/1919190 Bernoulli(38) 2929993913841559/6 Bernoulli(40) -261082718496449122051/13530 Bernoulli(42) 1520097643918070802691/1806 Bernoulli(44) -27833269579301024235023/690 Bernoulli(46) 596451111593912163277961/282 Bernoulli(48) -5609403368997817686249127547/46410 Bernoulli(50) 495057205241079648212477525/66 Bernoulli(52) -801165718135489957347924991853/1590 Bernoulli(54) 29149963634884862421418123812691/798 Bernoulli(56) -2479392929313226753685415739663229/870 Bernoulli(58) 84483613348880041862046775994036021/354 Bernoulli(60) -1215233140483755572040304994079820246041491/56786730 Bernoulli(62) 12300585434086858541953039857403386151/6 Bernoulli(64) -106783830147866529886385444979142647942017/510 Bernoulli(66) 1472600022126335654051619428551932342241899101/64722 Bernoulli(68) -78773130858718728141909149208474606244347001/30 Bernoulli(70) 1505381347333367003803076567377857208511438160235/4686 Bernoulli(72) -5827954961669944110438277244641067365282488301844260429/140100870 Bernoulli(74) 34152417289221168014330073731472635186688307783087/6 Bernoulli(76) -24655088825935372707687196040585199904365267828865801/30 Bernoulli(78) 414846365575400828295179035549542073492199375372400483487/3318 Bernoulli(80) -4603784299479457646935574969019046849794257872751288919656867/230010 Bernoulli(82) 1677014149185145836823154509786269900207736027570253414881613/498 Bernoulli(84) -2024576195935290360231131160111731009989917391198090877281083932477/3404310 Bernoulli(86) 660714619417678653573847847426261496277830686653388931761996983/6 Bernoulli(88) -1311426488674017507995511424019311843345750275572028644296919890574047/61410 Bernoulli(90) 1179057279021082799884123351249215083775254949669647116231545215727922535/ 272118 Bernoulli(92) 1295585948207537527989427828538576749659341483719435143023316326829946247/141 0 Bernoulli(94) 1220813806579744469607301679413201203958508415202696621436215105284649447/6 Bernoulli(96) 21160044959726651309759772810982423367304395438906023415063873342005066834998 7 259/4501770 Bernoulli(98) 67908260672905495624051117546403605607342195728504487509073961249992947058239 /6 Bernoulli(100) 94598037819122125295227433069493721872702841533066936133385696204311395415197 2 47711/33330 Bernoulli(102) 32040194108609070782430207821162417754918171971527174506790025010868615308366 78 158791/4326 Bernoulli(104) 31953363136383001128710335279617427467118960607827273832710347016284956836554 9 721224053/1590 Bernoulli(106) 36373903172617414408151820151593427169231298640581690038930816378281879873386 20 2346572901/642 Bernoulli(108) 34693422478478287895520886593238525413997667857604911468700058913715012663197 2 4897592306597338057/209191710 Bernoulli(110) 76459929404847428922481342467243475005287524134123079066835938707597976062695 85 779977930217515/1518 Bernoulli(112) 26508796021550997133525972146851620144431514991925098964517884276809667565148 7 5515366781203552600109/1671270 Bernoulli(114) 21737832319369163333310761086652991475721156679090831360806110114933605484234 59 3650904188618562649/42 Bernoulli(116) 30955391657184297691251345803384141686900412806432984424550404572100895752457 1 968271388199595754752259/1770 Bernoulli(118) 36696311996971311153494715158558500668460636108069920430105944067641448504580 64 61889371776354517095799/6 Bernoulli(120) 51507486535079109061843996857849983274095170353262675213092869167199297474922 9 85358811329367077682677803282070131/2328255930 Bernoulli(122) 49633666079262581912532637475990757438722790311060139770309311793150683214100 43 1329033113678098037968564431/6 Bernoulli(124) 95876775334247128750774903107542444620578830013297336819553512729358593354435 9 44413631943610268472689094609001/30 Bernoulli(126) 55563302819492748506163244089189513805255673071267472467967823043335942864005 08 981287241419934529638692081513802696639/4357878 Bernoulli(128) 26775470774254808288695440558528239477929145959255174062997868606335779273486 3 530145362663093519862048495908453718017/510 Bernoulli(130) 19282151751361309156452995222715964353076110101647284587837330205285486224035 04 078595174411693893882739334735142562418015/8646 Bernoulli(132) 41095194584699337820902048652357193812325807787047750243346974796265007075470 4 863812646392801863686694106805747335370312946831/4206930 Bernoulli(134) 26459017187071772563363573724887901515125452559316868841191855484066776559169 05 40727987316391252434348664694639349484190167/6 Bernoulli(136) 84290226343367405131287578060366193649336612397547435767189206912230442242628 2 12786558235455817749737691517685781164837036649737/4110 Bernoulli(138) 26948665489908809360438516837241130408490784946642824838621508930604785015595 46 243423633375693325757795709438325907154973590288136429/274386 Bernoulli(140) 32894909864358988039306995488518840068805374769311309813074670851625048029736 1 8096693859598125274741604181467826651144393874696601946049/679470 Bernoulli(142) 14731853280888589565870080442453214239804217023990642676194878997407546061581 64 3106569966189211748270209483494554402556608073385149191/6 Bernoulli(144) 30502446983736075650351558369017263574050071042565667618841918524348510337447 6 1276392695669329626855965183503295793517411526056244431024612640493/238171479 0 Bernoulli(146) 41205700262801148715261133159078640261655456088085411539738176800347902626835 24 284855810008621905238290240143481403022987037271683989824863/6 Bernoulli(148) 16917371456140189798655610951121661896076828521473014008164806759169578711786 4 8433284821493606361235973346584667336181793937950344828557898347149/4470 Bernoulli(150) 46336557938916274144328442581180626498223372542529579985229980732537931550157 23 05760030594769688296308375193913787703707693010224101613904227979066275/21626 22 Bernoulli(152) 37370181411551085021058928884912821658374895314889329517685071271824097313284 7 2084456653639812530140212355374618917309552824925858430886313795805601/30 Bernoulli(154) 10259718682038021051027794238379184461025738652460569233992776489750881337506 86 3808448685054322627708245455888249006715516690124228801409697850408284121/138 Bernoulli(156) 81718086083262628510756459753673452313595710396116467582152090596092548699138 3 46942995509488284650803976836337164670494733866559829768848363506624334818961 41 9869/1794590070 Bernoulli(158) 17167267690115321007218308350610339513751392227402956415050013526530814819735 85 51999205867870374013289728260984269623579880772408522396975250682773558018919 /6 Bernoulli(160) 42408607942033103760655634923611569499893980870863732147106257784584419404778 3 99818509288304200292856870667018046454531597674029612293059427657841224211977 36 180867/230010 Bernoulli(162) 15844514951444164283909342432794261408365964760807863169602223807842393809747 99 88036436364797816863459041821585441979371654938886590534853437562992873200878 62 33507729/130074 Bernoulli(164) 20538064609143216265571979586692646837805331023148645068133372383930344948316 6 00591203926388540940814833173322793804325084945094828524860626092013547281335 35 6200073083/2490 Bernoulli(166) 57340329693708609216310953113926457315052223585552084985730889113030017846521 22 96470320575270919419309524630861126412167883425070446808264831378812475416867 18 15815821441/1002 Bernoulli(168) 13844828515176396081238346585063517228531109156984345249260453934317772754836 7 91258987516540324983611569758649525983347408589045734176589270143058509026392 24 6407576578281097477/3404310 Bernoulli(170) 19533420762663753041497677923846223448141033735098842721513999570734697912468 69 18267688171536352650572535330369818176979951931477427594872783018749894699157 91 7782460035894085/66 Bernoulli(172) 11443702211333328447187179942991846613008046506032421731755258148665287832264 9 31024781365962633301701773088470841621804328201008020129996955549467573217659 58 7609679405537739509973/5190 Bernoulli(174) 41661615546620428318849595932507172973956143181825614120481806840774078033175 91 27083119461929383210748242694565514335790980725185285927948317637343569760763 98 83085093246499347128331/2478 Bernoulli(176) 13693479104867057076456213625128243322203607744765943483569387153666080445886 1 46575574361317065439484641599479704643460702532782919896963900968007996146173 17 655510118710460076077638883999/1043970 Bernoulli(178) 11242518166179412900264848512062999827747204677128672752920437016188298267083 95 74545965417071836318214341831451408542669285701842861493541273606394685303309 43 28968069656979232446257101741/1074 Bernoulli(180) 61731364540162489246405222722634709601995593282906553375302020558533977917473 4 13123470301419065009937527006122336959545328160182077217318182252900766702134 81 102834647254685911917265818955932383093313/7225713885390 Bernoulli(182) 42772692793491925411373044006286293483274681358284022916616830186224516599895 95 51071291581043623872113954696355865526038432898877321968809144352962653133568 79 51612545946030357929306651006711/6 Bernoulli(184) 85732133352305618013119443734793321643140330573070535901546564928568143231751 4 01068602907932447965963464238480906171131948102003071598900914059517055695619 67 62318625529645723516532076273012244047/1410 Bernoulli(186) 22258646098436968050639602221816385181596567918515338169946670500599612225742 48 75950127758383873315504747512122606361635000867874176409037708073532281574783 39 547041472679880890292167353534100797481/42 Bernoulli(188) 14158277750623758793309386870401397333112823632717478051426522029712001260747 9 20789473711562165031101665618225654329210473605281619696918061316240634857984 01 9071572591940586875558943580878119388321001/30 Bernoulli(190) 54115558425442597961318855461967872779878374866387561841491415887839897745115 09 60873342906751738375070629948682270217167252220310673099358124277782586420348 72 38429479957280273093904025319950569633979493395/12606 Bernoulli(192) 34646575299758269969019140575095236687192319234095559348648571537039215489410 2 00040698016252172849250191759801271140216353016651699111512213139854202905628 69 59857727373568402417020319761912636411646719477318166587/868841610 Bernoulli(194) 22691868251615329628336650869683599673893214292975883372329867524097654142234 76 69686319975998161181766073575383132390045649525396183717592431210887291508953 49 70310604331636484174526399721365966337809334021247/6 Bernoulli(196) 62753135110461193672553106699893713603153054153311895305590639107017824640241 3 78480484625554578576142115835788960865534532214560982925549798683762705231316 61 1716668749347221458005671217067357943416524984438771831113/171390 Bernoulli(198) 88527914861348004968400581010530565220544526400339548429439843908721196349579 49 40692822856626534659899202372531625556665263858264498628630838340968230530480 72 002986184254693991336699593468906111158296442729034119206322233/244713882 Bernoulli(200) 49838404942833341476492863214039966210849588745720667496805582261726366962152 3 68756886580230221099913260141269761327939105865452714534051584009929047802635 03 82802884371712359337984274122861159800280019110197888555893671151/1366530 Bernoulli(202) 22505253261872645459007144606288851358410504445512471162226314116815497805302 33 51606995753439457492257929060818042752031823562112368610947434388785794461184 24 38698399885295153935574958275021715116120056995036417537079471/6 Bernoulli(204) 11063664425085690359097648142279487920051723129954099471537233452112866971626 4 19633381102570974774619321078682011436902584989734572253109804276053092265687 88 91556664782168465095563132092311332073097630676251482491663634626858373/28119 0 Bernoulli(206) 25252926688914049202794270266689693894563882493898893394556043166915733842846 78 29362010006692436169366644472233874383919822134793165191680765119880093594249 30 38194104759967208073711284671045255047521429204396148980705984836743/6 Bernoulli(208) 12407390668433023412711473483696990726334795896412761472587854072142800403373 5 77087021298541061094633377354326966623278849423631924808044397822651135905640 81 2063181221280972334965193338438214107578486417026806166184210160001817890901/ 27030 Bernoulli(210) 47081813685294926141106441979518373172026106083412572042066931952412452043608 22 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92333376620144456976064549959350955465207852058394989331047026479739175484506 54 482159/63346038 Bernoulli(488) 10541816873814096381316169108539113544559806579137816926164708551453053764421 6 74476779663590418587721548805288914617597594086705240368673303934588475540778 05 02211337155151276130135366864188194331564067386241198640208470590827183303724 84 41148559758203373649679290148162009307104085713861437407027770249084665069566 42 48028186959784027234555083365255720079247979950886689963934128030067369716278 89 52261804853628790825262219805772152623963856175241322796137570926214113320444 86 16567780414625262935283998346756442958214463663418419136319815181399963230777 04 74159980792200412996991870674127149512046516569338215208475275772897223820007 54 06380443398804281537239686002151594593678805941545700491777795561018985343223 40 56001/30 Bernoulli(490) 49070806034571816848294955106500829697635234181215685091246075479377322859874 30 21163789697895339848508047563198613297970895771272423084451586762411542433689 88 48825822179201506153202612964126576554202949508824725190771074364118913149896 84 27282740514345366467629990128242774621400277601642928999273459694164702679454 28 62610180682813869753438462413802302318288921935542654412271101075502309306996 45 99725177158261320897365975843205116692637947011054170991764360555416227226118 53 66547942992924338227578513676078811847744437078135661673916775819224150771600 58 71662971992278037186350173271291067722673038829083878521474773044108789762491 72 63853209223974696199700464383784523903213675515116272067656164140406864509160 33 159995734945/2300826 Bernoulli(492) 29571068203636866046288982859461223295592495500220152470524852020659222298589 8 20846856440902464355266331921730127927945659951516772762515060645001891839736 58 66826625510003837807762234721907229268939728260753209578951485832358379661753 32 09050969370549540982453282828388206120029279998278753379433675825020205456689 56 50111341100127955540207905539288764843239635727038706673051411859354656143960 39 19778742559512015901475146476123141564243291327909428505227081149290897384800 80 97977295940813077959111257610340633735603719103411193071451187937622330746267 75 90891465762187531182727331935416048942500997565555024227597619955118636192752 51 19846700395907422799296606519248369841030425783198567324724905036753320437659 60 5858401058641353/226590 Bernoulli(494) 48304952056070024985817756788239978908682438355340656791822950062590796355241 24 66894489636117289385056013694632157195762896070359698773642254744021501072670 21 03347261763300249866673954071972606720890840086862947165242945807876848462643 92 83884479517280978247192859399400878296914805548929586054952054550941690046726 38 73853432524745078962055365592853439992861256734658389110188036769686342340589 96 14307645331900735834769509776964822414319141365122098841101236574197264513647 09 05240747776225223601701498704103140362659865756058524036705273180849600017203 42 26362765220595663439733476783625903396579749288087861502113858006100123874110 13 19522967529509678583347839242395803991809619445840333184984291808994467998793 56 90252652536647/6 Bernoulli(496) 25535109222241698972694173193973518774716242178265877234279078154218306288190 4 53574391345349607020347701104389306082727640662249328994752154372973422361999 09 27159227596335212703785415077907697633574562763787265956264597246236796039155 77 64394770047210667359358311843696006289416640231286719037659293148046402280224 09 67436286930003098509086131781553808335933575272888361402715107788113154287996 38 58614862072575318992227607627470867584738943963602175945843876568872310718111 45 64396011162845823277525352598381790749640760035718291974416252381371219543613 57 03038816616947504736640465073624938220282345566631808140813969037396579578863 66 37017142026831788287304419335827735140242183329158752591947675885070011498701 06 803558286434937883617/510 Bernoulli(498) 10986512284815158461167356059429016575444189427636856054838191284549763854648 99 43473724236724095238506744474900836564256806367057972840967346175127292454912 52 85602795045413203741844230426358616759853983294227411821897092348333446120995 75 63396163734906204465362988901675177097463287428702991573662953563900325769847 86 43655378973595019757875361471141167104505491430542529353951978597591329218845 84 35472840034103326532984267720997838197057411785852422605414587329459898626238 31 44316049831746659579206938157552277360135459297816030729856389236883243552993 38 79136847223915909126311223045236240031443275276664068708400030822980635517221 01 81524971644942859893996940410875091940649202106109066788663807627887433701124 81 7799811432100659519242101309/3499986 End of The Project Gutenberg Etext of The first 498 Bernoulli Numbers