The input for log(2) is: DelSeqSum(binomial(n,k)*binomial(n+k,k),k,n,100); the output is: .346573590279972654708616060729088284037750067180127627060340004746696810984847\ 3578029316634982093437710007405102853428668427601178790652785163353758175379809\ 6536378541418571759515351931194583673556167505768224897761956023758634078746603\ 2577762367069762941475226503547663183321327052119578907476021870, 1/2*ln(2), [1\ .469756893, 1.734670091, 1.415335766, 1.568714738, 1.418338072, 1.497216654, 1.\ 539990758, 1.573814966, 1.429769110, 1.461791290, 1.393431491, 1.462215072, 1.4\ 50100752, 1.586083915, 1.471265738, 1.500632758, 1.393267764, 1.410015370, 1.40\ 7076723, 1.581936340, 1.329863561, 1.383509486, 1.353106048, 1.342185435, 1.322\ 185856, 1.401419956, 1.348586243, 1.451839412, 1.352993007, 1.499717839, 1.4002\ 66619, 1.387005371, 1.367975003, 1.398920282, 1.390526719, 1.371529147, 1.37574\ 8984, 1.405563825, 1.352064459, 1.353226986, 1.399759822, 1.330963381, 1.318307\ 603, 1.356870508, 1.298868894, 1.396245179, 1.345749379, 1.380447379, 1.3804809\ 73, 1.369080196, 1.347769766, 1.368742799, 1.321059120, 1.373301027, 1.31817118\ 0, 1.358425205, 1.326893739, 1.390055744, 1.336344715, 1.361990523, 1.347686251 , 1.380172394, 1.335974428, 1.340778219, 1.336723038, 1.346927817, 1.339397229, 1.335465135, 1.343862560, 1.334309625, 1.330173612, 1.389965377, 1.297370247, 1\ .323793502, 1.283191919, 1.301126916, 1.337239076, 1.311831231, 1.315645016, 1.\ 354144842, 1.290853411, 1.351624570, 1.312704374, 1.347522139, 1.343416926, 1.3\ 61102033, 1.350225209, 1.357769387, 1.317725954, 1.327920026, 1.315932109] --------------------------- --------------------------- The input for Zeta(2) is: DelSeqSum(binomial(n,k)^2*binomial(n+k,k),k,n,100); the output is: .328986813369645287294483033329205037843789980241359687547111645874001494080640\ 1747667257801239517410608008637924674381359257449374010015575870205892661732553\ 6634666187355252101905020137442801095936231175897807216465555238396815129117539\ 2647127341942019389780417186401610327295775667769208889036811965, 1/30*Pi^2, [1\ .283156031, 1.851139415, 1.324606405, 1.439660249, 1.315738178, 1.350417527, 1.\ 252662677, 1.387599576, 1.249431714, 1.207940181, 1.159709753, 1.192695469, 1.2\ 78697774, 1.271909193, 1.190764690, 1.302728124, 1.173658847, 1.180656881, 1.22\ 8589193, 1.271823651, 1.143822921, 1.170965791, 1.169665336, 1.129952390, 1.136\ 278522, 1.213906307, 1.189618615, 1.226202082, 1.162201210, 1.281985762, 1.1798\ 65028, 1.264026617, 1.152127393, 1.177183442, 1.146457883, 1.150908408, 1.16042\ 7494, 1.209707845, 1.159044739, 1.141747174, 1.152252368, 1.147394394, 1.151204\ 018, 1.188235628, 1.129042288, 1.170975295, 1.152849908, 1.173513372, 1.2025330\ 38, 1.184390957, 1.180732593, 1.197077260, 1.127782535, 1.131106389, 1.14373476\ 2, 1.183472653, 1.153200474, 1.208707407, 1.156445633, 1.145274706, 1.161870778 , 1.216148181, 1.162770820, 1.146821644, 1.136685290, 1.128758433, 1.142034347, 1.145231807, 1.151419737, 1.158141662, 1.127853117, 1.165154745, 1.129322543, 1\ .169534912, 1.125718765, 1.122622647, 1.161855657, 1.134256536, 1.159605392, 1.\ 171409762, 1.120813383, 1.129567584, 1.123295777, 1.146370468, 1.147979648, 1.1\ 53805333, 1.157318081, 1.146540163, 1.137314007, 1.140684738, 1.133336201] --------------------------- --------------------------- The input for Zeta(3) is: DelSeqSum(binomial(n,k)^2*binomial(n+k,k)^2,k,n,100); the output is: .200342817193265714233289693585241665127497715390083146965378592556973034297718\ 8483644093122682225430243665262992101199030819993331122138689627328062013166935\ 7565696382489334445319859592037374904066026065161068388185984929682758577521331\ 9734184285875998002572851630183673304588761131267253722830823610, 1/6*Zeta(3), [1.271120671, 1.322440843, 1.313014933, 1.257564459, 1.219634020, 1.206923726, 1.240958676, 1.300429497, 1.167713807, 1.240475702, 1.153200543, 1.224063207, 1\ .255374935, 1.260963403, 1.207920070, 1.214527246, 1.181272198, 1.234207656, 1.\ 238070507, 1.211876187, 1.167546127, 1.194253699, 1.137821866, 1.132291186, 1.1\ 56759114, 1.162380658, 1.167725063, 1.199517454, 1.152830422, 1.180269384, 1.16\ 8947312, 1.172435890, 1.140097379, 1.162329963, 1.131587276, 1.136263132, 1.140\ 764689, 1.170531653, 1.127809922, 1.144868906, 1.110970112, 1.112556710, 1.1413\ 46088, 1.132048859, 1.118058927, 1.139466561, 1.148509755, 1.164208624, 1.16067\ 0405, 1.169205287, 1.143234261, 1.139013782, 1.113040678, 1.111950961, 1.129053\ 442, 1.129837916, 1.158886674, 1.155280067, 1.126956236, 1.141688215, 1.1336760\ 21, 1.141350830, 1.143222954, 1.114136528, 1.094171125, 1.097227054, 1.11387686\ 5, 1.114208456, 1.116985877, 1.133034577, 1.106058658, 1.115846625, 1.119696767 , 1.121313646, 1.097644100, 1.113489226, 1.102917850, 1.121357066, 1.114469320, 1.132497920, 1.099197503, 1.107855209, 1.118489419, 1.120977001, 1.133926031, 1\ .124488062, 1.132267143, 1.140515715, 1.116950377, 1.130176579, 1.127050871] --------------------------- --------------------------- a random (disappointing) input is: DelSeqSum(binomial(n,k)^2*binomial(n+k,k)*2^k,k,n,100); the output is: .226657372775579392144395157413753142002650116407559374448788982021599045595037\ 1910032252154176039945754510450345382011649810787985679496722402990990676032311\ 4062113705458666269859595698023085552741025800444088323884475747833393767608600\ 6962127630022158608400269443853430808903960758379408676491027128e-1, .\ 22665737277557939214e-1, [.6318061543, .5941341279, .6199078174, .5902698166, .\ 5337609502, .5480945775, .5611827505, .6064116121, .5319225125, .5504282611, .5\ 353190594, .5337037938, .5643175555, .5632822430, .5373085005, .5568906134, .55\ 62611361, .5744253865, .5446855434, .5430900060, .5224348088, .5366643010, .516\ 2381529, .5122313591, .5249521048, .5242564973, .5405057019, .5407661162, .5301\ 156720, .5234906951, .5285954136, .5612258327, .5218935075, .5222919210, .50762\ 10035, .5170535271, .5166953906, .5417698912, .5190174765, .5186351830, .513898\ 9313, .5300941760, .5305639917, .5290313228, .5093096662, .5256155957, .5310156\ 409, .5279885811, .5347676279, .5469253538, .5220762638, .5283075027, .51699152\ 81, .5138682508, .5294515208, .5299931916, .5280825092, .5354499068, .517745801\ 6, .5206787195, .5166827295, .5164448777, .5085992926, .5162707286, .4977470488 , .5004969773, .5059408257, .5180497664, .5175244362, .5151895670, .5129448805, .5103988030, .5180607659, .5174716452, .5019724169, .5068398362, .5109058698, .\ 5193395004, .5163861773, .5141136258, .5054386012, .5100033220, .5143666475, .5\ 097848535, .5195815077, .5140761322, .5127756409, .5189676895, .5066660118, .50\ 87216688, .5107521300] --------------------------- --------------------------- a random (good!) input is: DelSeqSum(binomial(n,k)*binomial(2*n+2*k,2*k)*11^k,k,n,100); the output is: .113597149435491831843110548929515417998053721661858566858128742448422920763073\ 6502274461851360738640331935589615037722008300602422976811976687928072803883475\ 5242632033211417840284772689334737406028331938577147333418891680837671272453824\ 4418079630969617574655066477728168738391587612942967613337795861e-3, .\ 11359714943549183184e-3, [1.149163510, 1.164372026, 1.192516162, 1.137526385, 1\ .134850257, 1.143312939, 1.169246984, 1.149624258, 1.130085292, 1.131870874, 1.\ 120312550, 1.153112352, 1.117492015, 1.121193240, 1.153883916, 1.113820075, 1.1\ 53207353, 1.147346546, 1.117099824, 1.149405970, 1.184009142, 1.143471497, 1.15\ 1491205, 1.139323384, 1.145385063, 1.143340834, 1.128468664, 1.119645054, 1.130\ 536828, 1.135037140, 1.135787470, 1.134269542, 1.133150635, 1.115441015, 1.1273\ 19463, 1.136721635, 1.118883055, 1.137963300, 1.137737016, 1.138955261, 1.13431\ 4542, 1.152845362, 1.140447257, 1.129701452, 1.143684324, 1.137301066, 1.124478\ 753, 1.122082511, 1.114816401, 1.122129086, 1.131707239, 1.138161727, 1.1455733\ 24, 1.142250343, 1.133452394, 1.130168178, 1.134005229, 1.127628088, 1.14935459\ 3, 1.155136060, 1.137329449, 1.143213392, 1.129534736, 1.141402652, 1.139893127 , 1.150051920, 1.154252156, 1.136278361, 1.127231172, 1.139432110, 1.136308516, 1.138478359, 1.121947961, 1.126018269, 1.127927072, 1.122957847, 1.131302126, 1\ .118797209, 1.119482807, 1.125629466, 1.128625888, 1.136332771, 1.114532706, 1.\ 120143496, 1.120508799, 1.121774892, 1.118544030, 1.112841566, 1.125872918, 1.1\ 25629114, 1.125952366] --------------------------- This took, 3.695, seconds.