A121673 a(n) = [x^n] (1 + x*(1+x)^(n-1) )^n.

1, 1, 3, 16, 131, 1306, 15257, 203967, 3047907, 50115310, 896746169, 17308420306, 357767229778, 7872926416538, 183537476164902, 4513828442107368, 116688468769638435, 3160881019508153238, 89471871451166037425

Offset: 0

Author

Paul D. Hanna, Aug 15 2006

Keywords

• nonn

Examples

			At n=4, a(4) = [x^4] (1 + x*(1+x)^3 )^4 = 131, since
(1 + x*(1+x)^3 )^4 = 1 + 4*x + 18*x^2 + 52*x^3 + 131*x^4 +...
		

Crossrefs

Cf. variants: A121674-A121680.

Programs

Mathematica

Table[Sum[Binomial[n,k] * Binomial[(n-1)*k,n-k], {k,0,n}], {n, 0, 20}] (* Vaclav Kotesovec, Jun 12 2015 *)

PARI

a(n)=sum(k=0,n,binomial(n,k)*binomial((n-1)*k,n-k))

Formula

a(n) = Sum_{k=0..n} C(n,k) * C((n-1)*k,n-k).