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