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