A121677 a(n) = A121676(n)/(n+1) = [x^n] (1 + x*(1+x)^(n-1) )^(n+1) / (n+1).

1, 1, 2, 8, 50, 402, 3932, 45075, 588450, 8580542, 137799497, 2410575026, 45531000715, 921946835474, 19895218322982, 455271977561120, 11000793881924130, 279648297003419318, 7454931579222301709

Offset: 0

Author

Paul D. Hanna, Aug 15 2006

Keywords

• nonn

Examples

			At n=4, a(4) = [x^4] (1 + x*(1+x)^3 )^5/5 = 250/5 = 50, since
(1 + x*(1+x)^3 )^5 = 1 + 5*x + 25*x^2 + 85*x^3 + 250*x^4 +...
		

Crossrefs

Cf. A121676; variants: A121673-A121675, A121678-A121680.

Programs

Mathematica

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

PARI

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

Formula

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