A121677 a(n) = A121676(n)/(n+1) = [x^n] (1 + x*(1+x)^(n-1) )^(n+1) / (n+1).

1, 1, 2, 8, 50, 402, 3932, 45075, 588450, 8580542, 137799497, 2410575026, 45531000715, 921946835474, 19895218322982, 455271977561120, 11000793881924130, 279648297003419318, 7454931579222301709

Offset

0,3

Links

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

Formula

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

Example

At n=4, a(4) = [x^4] (1 + x*(1+x)^3 )^5/5 = 250/5 = 50, since
(1 + x*(1+x)^3 )^5 = 1 + 5*x + 25*x^2 + 85*x^3 + 250*x^4 +...

Mathematica

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

Prog

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

Crossrefs

Cf. A121676; variants: A121673-A121675, A121678-A121680.

Sequence in context: A231352 A186182 A274273 * A120956 A000557 A193352

Adjacent sequences: A121674 A121675 A121676 * A121678 A121679 A121680

Keyword

nonn

Author

Paul D. Hanna, Aug 15 2006

Status

approved