This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A005429 M2169 #51 Nov 20 2022 08:35:13
%S A005429 0,2,48,540,4480,31500,199584,1177176,6589440,35443980,184756000,
%T A005429 938929992,4672781568,22850118200,110079950400,523521630000,
%U A005429 2462025277440,11465007358860,52926189069600,242433164404200,1102772230560000,4984806175188840,22404445765690560
%N A005429 Apéry 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).
%H A005429 T. D. Noe, <a href="/A005429/b005429.txt">Table of n, a(n) for n=0..200</a>
%H A005429 M. Kondratiewa and S. Sadov, <a href="https://arxiv.org/abs/math/0405592">Markov's transformation of series and the WZ method</a>, arXiv:math/0405592 [math.CA], 2004.
%H A005429 A. J. van der Poorten, <a href="http://dx.doi.org/10.1007/BF03028234">A proof that Euler missed ... Apery's proof of the irrationality of zeta(3)</a>, Math. Intelligencer 1 (1978/1979), 195-203.
%H A005429 I. J. Zucker, <a href="http://dx.doi.org/10.1016/0022-314X(85)90019-8">On the series Sum(k>=1) C(2k,k)^(-1)*k^(-n) and related sums</a>, J. Number Theory 20 (1985), no. 1, 92-102.
%F A005429 Sum_{n>=1} (-1)^(n+1) / a(n) = 2 * zeta(3) / 5.
%F A005429 G.f.: (2*x*(2*x*(2*x + 5) + 1))/(1-4*x)^(7/2). - _Harvey P. Dale_, Apr 08 2012
%F A005429 From _Ilya Gutkovskiy_, Jan 17 2017: (Start)
%F A005429 a(n) ~ 4^n*n^(5/2)/sqrt(Pi).
%F A005429 Sum_{n>=1} 1/a(n) = (1/2)*4F3(1,1,1,1; 3/2,2,2; 1/4) = A145438. (End)
%t A005429 Table[n^3 Binomial[2n,n],{n,0,30}] (* _Harvey P. Dale_, Apr 08 2012 *)
%t A005429 CoefficientList[Series[(2*x*(2*x*(2*x+5)+1))/(1-4*x)^(7/2), {x,0,30}], x] (* _Vincenzo Librandi_, Oct 22 2014 *)
%o A005429 (Magma) [Binomial(2*n,n)*n^3 : n in [0..30]]; // _Wesley Ivan Hurt_, Oct 21 2014
%o A005429 (SageMath) [n^3*binomial(2*n,n) for n in range(31)] # _G. C. Greubel_, Nov 19 2022
%Y A005429 Cf. A002736, A005258, A005259, A005429, A005430, A145438.
%K A005429 nonn,nice,easy
%O A005429 0,2
%A A005429 _Simon Plouffe_
%E A005429 Entry revised by _N. J. A. Sloane_, Apr 06 2004