Search: id:A002736
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%I A002736 M2136 N0848
%S A002736 0,2,24,180,1120,6300,33264,168168,823680,3938220,18475600,85357272,
%T A002736 389398464,1757701400,7862853600,34901442000,153876579840,674412197580,
%U A002736 2940343837200,12759640231800,55138611528000,237371722628040,1018383898440480
%N A002736 Ap\*'ery numbers: n^2 C(2n,n).
%C A002736 sum(n=1,inf,1/a(n))=Pi^2/18 (Euler) - Benoit Cloitre (benoit7848c(AT)orange.fr), 
               Apr 07 2002
%D A002736 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A002736 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A002736 J. Ser, Les Calculs Formels des S\'{e}ries de Factorielles. Gauthier-Villars, 
               Paris, 1933, p. 93.
%D A002736 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.
%H A002736 T. D. Noe, <a href="b002736.txt">Table of n, a(n) for n=0..200</a>
%H A002736 H. J. H. Tuenter, <a href="http://arXiv.org/abs/math.NT/0606080">Walking 
               into an absolute sum</a>
%p A002736 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
%o A002736 (Mupad) combinat::catalan(n)*(n+1)*n^2 $ n = 0..36 - Zerinvary Lajos 
               (zerinvarylajos(AT)yahoo.com), Apr 17 2007
%Y A002736 Cf. A002736, A005258, A005259, A005429, A005430.
%Y A002736 Sequence in context: A157053 A052411 A073066 this_sequence A131972 A059387 
               A126190
%Y A002736 Adjacent sequences: A002733 A002734 A002735 this_sequence A002737 A002738 
               A002739
%K A002736 nonn,easy,nice
%O A002736 0,2
%A A002736 N. J. A. Sloane (njas(AT)research.att.com).

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