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 A002018 M3652 N1485 #34 Apr 24 2025 04:32:25
%S A002018 1,1,4,33,480,11010,367560,16854390,1016930880,78124095000,
%T A002018 7446314383200,862332613342200,119261328828364800,
%U A002018 19415283189746043600,3675162134109650184000,800409618620667941886000,198730589981586780813696000,55800304882692417053710704000
%N A002018 From a distribution problem.
%D A002018 H. Anand, V. C. Dumir and H. Gupta, A combinatorial distribution problem, Duke Math. J., 33 (1996), 757-769.
%D A002018 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A002018 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A002018 Seiichi Manyama, <a href="/A002018/b002018.txt">Table of n, a(n) for n = 0..253</a>
%F A002018 a(n) = n*(2*n-1)*b(n-1) - n*(n-1)^2*b(n-2), b(n) = A000681(n). [corrected by _Seiichi Manyama_, Apr 22 2025]
%F A002018 From _Seiichi Manyama_, Apr 22 2025: (Start)
%F A002018 a(n) = (n-1)! * n! * Sum_{k=0..n-1} (-1)^k * (1/2)^(n-k-1) * binomial(-3/2,k)/(n-k-1)! for n > 0.
%F A002018 a(n) = (n-1)! * n! * [x^(n-1)] 1/(1-x)^(3/2) * exp(x/2) for n > 0.
%F A002018 a(n) = n * ( n*a(n-1) - (n-1)*(n-2)/2 * a(n-2) ) for n > 1. (End)
%F A002018 a(n) ~ 4 * sqrt(Pi) * n^(2*n + 1/2) / exp(2*n - 1/2). - _Vaclav Kotesovec_, Apr 24 2025
%t A002018 b[n_] := Sum[(2i)!*n!^2/(2^i*i!^2*(n-i)!), {i, 0, n}]/2^n; a[n_] := n*(2n-1)*b[n-1] - n*(n-1)^2*b[n-2]; a[0]=1; Table[a[n], {n, 0, 17}] (* _Jean-François Alcover_, Aug 08 2012, after formula *)
%Y A002018 Cf. A000681.
%K A002018 nonn,easy,nice
%O A002018 0,3
%A A002018 _N. J. A. Sloane_
%E A002018 More terms from _David W. Wilson_