A121674 a(n) = [x^n] (1 + x*(1+x)^n )^n.

1, 1, 5, 28, 233, 2376, 28102, 379016, 5707025, 94439440, 1699067321, 32951077193, 684009742319, 15110032165151, 353485501643471, 8721374385748256, 226128389777924385, 6142306518887606112, 174311816444805024379

Offset: 0

Author

Paul D. Hanna, Aug 15 2006

Keywords

• nonn

Examples

			At n=4, a(4) = [x^4] (1 + x*(1+x)^4 )^4 = 233, since
(1 + x*(1+x)^4 )^4 = 1 + 4*x + 22*x^2 + 76*x^3 + 233*x^4 +...
		

Links

• Paul D. Hanna, Table of n, a(n) for n = 0..300

Crossrefs

Cf. variants: A121673, A121675-A121680.

Programs

Mathematica

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

PARI

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

Formula

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