Revision History for A024397
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Showing entries 1-10
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| A024397
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a(n) = s(1)*s(2)*...*s(n+1)*(1/s(2) - 1/s(3) + ... + c/s(n+1)), where c = (-1)^(n+1) and s(k) = 3k-1 for k = 1,2,3,...
(history;
published version)
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#12 by Vaclav Kotesovec at Thu Jan 02 04:07:18 EST 2020
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#11 by Vaclav Kotesovec at Thu Jan 02 04:06:56 EST 2020
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| FORMULA
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a(n) ~ Gamma(1/3) * (9 - 2*Pi*sqrt(3) + 6*log(2)) * 3^(n - 1/2) * n^(n + 7/6) / (2^(3/2) * sqrt(Pi) * exp(n)). - Vaclav Kotesovec, Jan 02 2020
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#10 by Vaclav Kotesovec at Thu Jan 02 04:05:28 EST 2020
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| MATHEMATICA
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Table[Product[3*k - 1, {k, 1, n+1}] * Sum[(-1)^k/(3*k - 1), {k, 2, n+1}], {n, 1, 20}] (* Vaclav Kotesovec, Jan 02 2020 *)
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| STATUS
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approved
editing
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#9 by N. J. A. Sloane at Thu Jan 02 00:36:39 EST 2020
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#8 by Andrew Howroyd at Wed Jan 01 23:34:10 EST 2020
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#7 by Andrew Howroyd at Wed Jan 01 23:33:56 EST 2020
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#6 by Andrew Howroyd at Wed Jan 01 23:20:51 EST 2020
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#5 by Andrew Howroyd at Wed Jan 01 23:12:59 EST 2020
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| NAME
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a(n) = s(1)*s(2)*...*s(n+1)*(1/s(2) - 1/s(3) + ... + c/s(n+1)), where c = (-1)^(n+1) and s(k) = 3k-1 for k = 1,2,3,...
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| DATA
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2, 6, 146, 1164, 32108, 432720, 14141360, 271332960, 10373558240, 259311694080, 11400458720000, 351858201408000, 17517836995904000, 644027147554560000, 35846613866733824000, 1530195810548224512000, 94207122098479233536000, 4580941398125400354816000
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| LINKS
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Andrew Howroyd, <a href="/A024397/b024397.txt">Table of n, a(n) for n = 1..100</a>
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| PROG
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(PARI) a(n)={my(s=vector(n+1, k, 3*k-1)); vecprod(s)*sum(k=2, #s, (-1)^k/s[k])} \\ Andrew Howroyd, Jan 01 2020
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| CROSSREFS
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Cf. A024384.
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| EXTENSIONS
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Terms a(11) and beyond from Andrew Howroyd, Jan 01 2020
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| STATUS
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approved
editing
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#4 by Russ Cox at Fri Mar 30 18:55:54 EDT 2012
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Discussion
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| Fri Mar 30
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| OEIS Server: https://oeis.org/edit/global/285
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#3 by N. J. A. Sloane at Fri May 16 03:00:00 EDT 2003
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| KEYWORD
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nonn,new
nonn
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| AUTHOR
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Clark Kimberling (ck6@cedar.(AT)evansville.edu)
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