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

1, 2, 12, 76, 655, 6816, 81690, 1109816, 16782399, 278438740, 5016899833, 97368894756, 2021749249403, 44658312247290, 1044437050070340, 25757381769393392, 667470006331599523, 18119105978249333988

Offset: 0

Author

Paul D. Hanna, Aug 15 2006

Keywords

• nonn

Comments

a(n) is divisible by (n+1): a(n)/(n+1) = A121681(n).

Examples

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

Crossrefs

Cf. A121681; variants: A121673-A121679.

Programs

Mathematica

Table[Sum[Binomial[n+1,k] * Binomial[(n+1)*k,n-k], {k,0,n+1}], {n,0,20}] (* Vaclav Kotesovec, Oct 02 2020 *)

PARI

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

Formula

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