Search: id:A005429
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%I A005429 M2169
%S A005429 0,2,48,540,4480,31500,199584,1177176,6589440,35443980,184756000,938929992,
%T A005429 4672781568,22850118200,110079950400,523521630000,2462025277440,11465007358860,
%U A005429 52926189069600,242433164404200,1102772230560000,4984806175188840,22404445765690560
%N A005429 Ap\*'ery numbers: n^3*C(2n,n).
%D A005429 S. R. Finch, Mathematical Constants, Cambridge, 2003, Section 1.6.3.
%D A005429 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A005429 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.
%D A005429 I. J. Zucker, On the series $ Sum\sp \infty\sb {k=1}(\sp{2k}\sb {\; k})\sp 
               {-1}k\sp{-n}$ and related sums, J. Number Theory 20 (1985), no. 1, 
               92-102.
%H A005429 T. D. Noe, <a href="b005429.txt">Table of n, a(n) for n=0..200</a>
%H A005429 M. Kondratiewa and S. Sadov, <a href="http://arXiv.org/abs/math.CA/0405592">
               Markov's transformation of series and the WZ method</a>
%F A005429 Sum_{ n >= 1} (-1)^(n+1) / a(n) = 2 zeta(3) / 5.
%p A005429 with(combinat):for n from 0 to 22 do printf(`%d, `,n^2*sum(binomial(2*n, 
               n), k=1..n)) od: - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Mar 13 2007
%Y A005429 Cf. A002736, A005258, A005259, A005429, A005430.
%Y A005429 Sequence in context: A101362 A058090 A051252 this_sequence A035606 A157057 
               A009670
%Y A005429 Adjacent sequences: A005426 A005427 A005428 this_sequence A005430 A005431 
               A005432
%K A005429 nonn,nice,easy
%O A005429 0,2
%A A005429 Simon Plouffe (simon.plouffe(AT)gmail.com)
%E A005429 Entry revised by N. J. A. Sloane (njas(AT)research.att.com), Apr 06 2004

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