|
%I #9 Nov 25 2021 10:46:51
%S 1,2,16,222,4416,114660,3676814,140408338,6222858240,314006546124,
%T 17774855765140,1115507717954432,76871991664546170,
%U 5770732305836768712,468750121409142448386,40964179307489016777630,3832326196169482368117760
%N Binomial convolution of the central Stirling numbers of the second kind.
%F a(n) = Sum_{k=0..n} binomial(n,k) * S(2k,k) * S(2n-2k,n-k).
%F Limit n->infinity (a(n)/n!)^(1/n) = -4/(LambertW(-2*exp(-2))*(2+LambertW(-2*exp(-2)))) = 6.17655460948348... . - _Vaclav Kotesovec_, Jun 01 2015
%p seq(sum(binomial(n, k) *combinat[stirling2](2*k, k) *combinat[stirling2](2*(n-k), n-k), k=0..n), n=0..12);
%t Table[Sum[Binomial[n, k]StirlingS2[2k, k]StirlingS2[2n - 2k, n - k], {k, 0, n}], {n, 0, 16}]
%o (Maxima) makelist(sum(binomial(n,k)*stirling2(2*k,k)*stirling2(2*n-2*k, n-k),k,0,n),n,0,12);
%K nonn,easy
%O 0,2
%A _Emanuele Munarini_, Mar 12 2011
|
