A121681 a(n) = A121680(n)/(n+1) = [x^n] (1 + x*(1+x)^(n+1) )^(n+1) / (n+1).

1, 1, 4, 19, 131, 1136, 11670, 138727, 1864711, 27843874, 456081803, 8114074563, 155519173031, 3189879446235, 69629136671356, 1609836360587087, 39262941548917619, 1006616998791629666, 27044968746461571213

Offset: 0

Author

Paul D. Hanna, Aug 15 2006

Keywords

• nonn

Examples

			At n=4, a(4) = [x^4] (1 + x*(1+x)^5 )^5 /5 = 655/5 = 131, since
(1 + x*(1+x)^5 )^5 = 1 + 5*x + 35*x^2 + 160*x^3 + 655*x^4 +...
		

Crossrefs

Cf. A121680; variants: A121673-A121679.

Programs

Mathematica

Table[Sum[Binomial[n+1,k] * Binomial[(n+1)*k,n-k] / (n+1), {k,0,n+1}], {n, 0, 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).