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%I #5 Jun 12 2015 05:46:07
%S 1,1,3,16,131,1306,15257,203967,3047907,50115310,896746169,
%T 17308420306,357767229778,7872926416538,183537476164902,
%U 4513828442107368,116688468769638435,3160881019508153238,89471871451166037425
%N a(n) = [x^n] (1 + x*(1+x)^(n-1) )^n.
%F a(n) = Sum_{k=0..n} C(n,k) * C((n-1)*k,n-k).
%e At n=4, a(4) = [x^4] (1 + x*(1+x)^3 )^4 = 131, since
%e (1 + x*(1+x)^3 )^4 = 1 + 4*x + 18*x^2 + 52*x^3 + 131*x^4 +...
%t Table[Sum[Binomial[n,k] * Binomial[(n-1)*k,n-k], {k,0,n}], {n, 0, 20}] (* _Vaclav Kotesovec_, Jun 12 2015 *)
%o (PARI) a(n)=sum(k=0,n,binomial(n,k)*binomial((n-1)*k,n-k))
%Y Cf. variants: A121674-A121680.
%K nonn
%O 0,3
%A _Paul D. Hanna_, Aug 15 2006
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