OFFSET
0,3
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
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Aug 15 2006
STATUS
approved