A121679 a(n) = A121678(n)/(n+1) = [x^n] (1 + x*(1+x)^n )^(n+1) / (n+1).

1, 1, 3, 13, 85, 706, 7042, 81887, 1081257, 15911488, 257476901, 4533396418, 86110501919, 1752312402881, 37982176570353, 872648321081531, 21162807249523025, 539772371783003416, 14433746294326451095

Offset: 0

Author

Paul D. Hanna, Aug 15 2006

Keywords

• nonn

Examples

			At n=5, a(5) = [x^5] (1 + x*(1+x)^5)^6/6 = 4236/6 = 706, since
(1+x*(1+x)^5)^6 = 1 + 6*x + 45*x^2 + 230*x^3 + 1050*x^4 + 4236*x^5 +...
		

Crossrefs

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

Programs

Mathematica

Table[Sum[Binomial[n+1,k] * Binomial[n*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*k,n-k))/(n+1)

Formula

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