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 A099021 #15 Oct 20 2012 20:38:59
%S A099021 1,1,4,24,198,2070,26160,387240,6565020,125341020,2659925520,
%T A099021 62089917120,1580632348680,43571319671880,1292731109429760,
%U A099021 41068078953501600,1390717740470058000,50003952605673066000,1902359109096675028800,76341746199227491382400
%N A099021 Main diagonal of array in A099020.
%C A099021 Diagonal of Euler-Seidel matrix with start sequence A001147.
%H A099021 Alois P. Heinz, <a href="/A099021/b099021.txt">Table of n, a(n) for n = 0..150</a>
%F A099021 a(n) = (1/(sqrt(2*Pi)))*Int(exp(-x^2/2)*(x(1+x))^n,x,-infinity,infinity). - _Paul Barry_, Apr 19 2010
%F A099021 Contribution from _Vaclav Kotesovec_, Oct 14 2012: (Start)
%F A099021 E.g.f.: exp(x^2/(2-4*x))/sqrt(1-2*x).
%F A099021 Recurrence: a(n) = (4*n-3)*a(n-1) - (n-1)*(4*n-7)*a(n-2) - (n-2)*(n-1)*a(n-3).
%F A099021 a(n) ~ 2^(n-1/2)*exp(sqrt(n/2)-n-3/16)*n^n.
%F A099021 (End)
%p A099021 a:= proc(n) a(n):= `if`(n<3, [1, 1, 4][n+1],
%p A099021 (4*n-3)*a(n-1) -(n-1)*(4*n-7)*a(n-2) -(n-2)*(n-1)*a(n-3))
%p A099021 end:
%p A099021 seq (a(n), n=0..20); # _Alois P. Heinz_, Oct 20 2012
%t A099021 Table[n!*SeriesCoefficient[E^(x^2/(2-4*x))/Sqrt[1-2*x],{x,0,n}],{n,0,20}] (* _Vaclav Kotesovec_, Oct 14 2012 *)
%K A099021 nonn
%O A099021 0,3
%A A099021 _Ralf Stephan_, Sep 23 2004