A121679 - OEIS

%I #5 Jun 12 2015 05:49:01

%S 1,1,3,13,85,706,7042,81887,1081257,15911488,257476901,4533396418,

%T 86110501919,1752312402881,37982176570353,872648321081531,

%U 21162807249523025,539772371783003416,14433746294326451095

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

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

%e At n=5, a(5) = [x^5] (1 + x*(1+x)^5)^6/6 = 4236/6 = 706, since

%e (1+x*(1+x)^5)^6 = 1 + 6*x + 45*x^2 + 230*x^3 + 1050*x^4 + 4236*x^5 +...

%t 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 *)

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

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

%K nonn

%O 0,3

%A _Paul D. Hanna_, Aug 15 2006