A121675 a(n) = [x^n] (1 + x*(1+x)^(n+1) )^n.

1, 1, 7, 43, 371, 3926, 47622, 654151, 9999523, 167557174, 3046387103, 59616689595, 1247357472869, 27747682830531, 653192297754076, 16206706672425167, 422358302959175123, 11526119161103900834

Offset

0,3

Links

Table of n, a(n) for n=0..17.

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)^5 )^4 = 371, since
(1 + x*(1+x)^5 )^4 = 1 + 4*x + 26*x^2 + 104*x^3 + 371*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: A121673, A121674, A121676-A121680.

Sequence in context: A164775 A127999 A208595 * A243273 A292502 A294361

Adjacent sequences: A121672 A121673 A121674 * A121676 A121677 A121678

Keyword

nonn

Author

Paul D. Hanna, Aug 15 2006

Status

approved