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Search: id:A002736
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| A002736 |
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Ap\*'ery numbers: n^2 C(2n,n).
(Formerly M2136 N0848)
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+0
11
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| 0, 2, 24, 180, 1120, 6300, 33264, 168168, 823680, 3938220, 18475600, 85357272, 389398464, 1757701400, 7862853600, 34901442000, 153876579840, 674412197580, 2940343837200, 12759640231800, 55138611528000, 237371722628040, 1018383898440480
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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sum(n=1,inf,1/a(n))=Pi^2/18 (Euler) - Benoit Cloitre (benoit7848c(AT)orange.fr), Apr 07 2002
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
J. Ser, Les Calculs Formels des S\'{e}ries de Factorielles. Gauthier-Villars, Paris, 1933, p. 93.
A. J. van der Poorten, A proof that Euler missed...Apery's proof of the irrationality of zeta(3), Math. Intelligencer 1 (1978/1979), 195-203.
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LINKS
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T. D. Noe, Table of n, a(n) for n=0..200
H. J. H. Tuenter, Walking into an absolute sum
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MAPLE
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with(combinat):for n from 0 to 22 do printf(`%d, `, n*sum(binomial(2*n, n), k=1..n)) od: - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 13 2007
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PROGRAM
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(Mupad) combinat::catalan(n)*(n+1)*n^2 $ n = 0..36 - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 17 2007
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CROSSREFS
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Cf. A002736, A005258, A005259, A005429, A005430.
Adjacent sequences: A002733 A002734 A002735 this_sequence A002737 A002738 A002739
Sequence in context: A157053 A052411 A073066 this_sequence A131972 A059387 A126190
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KEYWORD
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nonn,easy,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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