A121679 a(n) = A121678(n)/(n+1) = [x^n] (1 + x*(1+x)^n )^(n+1) / (n+1).

1, 1, 3, 13, 85, 706, 7042, 81887, 1081257, 15911488, 257476901, 4533396418, 86110501919, 1752312402881, 37982176570353, 872648321081531, 21162807249523025, 539772371783003416, 14433746294326451095

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*k,n-k) / (n+1).

Example

At n=5, a(5) = [x^5] (1 + x*(1+x)^5)^6/6 = 4236/6 = 706, since
(1+x*(1+x)^5)^6 = 1 + 6*x + 45*x^2 + 230*x^3 + 1050*x^4 + 4236*x^5 +...

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A377966 A369550 A125500 * A349582 A246387 A023037

Adjacent sequences: A121676 A121677 A121678 * A121680 A121681 A121682

Keyword

nonn

Author

Paul D. Hanna, Aug 15 2006

Status

approved