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

0,3

Links

Table of n, a(n) for n=0..18.

Formula

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

Example

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 +...

Mathematica

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

Prog

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

Crossrefs

Cf. variants: A121674-A121680.

Sequence in context: A120021 A223897 A131490 * A273997 A051921 A023998

Adjacent sequences: A121670 A121671 A121672 * A121674 A121675 A121676

Keyword

nonn

Author

Paul D. Hanna, Aug 15 2006

Status

approved