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%I #3 Mar 30 2012 18:36:58
%S 1,2,6,32,250,2412,27524,360600,5296050,85805420,1515794467,
%T 28926900312,591903009295,12907255696636,298428274844730,
%U 7284351640977920,187013495992710210,5033669346061547724,141643700005223732471
%N a(n) = [x^n] (1 + x*(1+x)^(n-1) )^(n+1).
%C a(n) is divisible by (n+1): a(n)/(n+1) = A121677(n).
%F a(n) = Sum_{k=0..n+1} C(n+1,k) * C((n-1)*k,n-k).
%e At n=4, a(4) = [x^4] (1 + x*(1+x)^3 )^5 = 250, since
%e (1 + x*(1+x)^3 )^5 = 1 + 5*x + 25*x^2 + 85*x^3 + 250*x^4 +...
%o (PARI) a(n)=sum(k=0,n+1,binomial(n+1,k)*binomial((n-1)*k,n-k))
%Y Cf. A121677; variants: A121673-A121675, A121678-A121680.
%K nonn
%O 0,2
%A _Paul D. Hanna_, Aug 15 2006
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