A121676 a(n) = [x^n] (1 + x*(1+x)^(n-1) )^(n+1).
1, 2, 6, 32, 250, 2412, 27524, 360600, 5296050, 85805420, 1515794467, 28926900312, 591903009295, 12907255696636, 298428274844730, 7284351640977920, 187013495992710210, 5033669346061547724, 141643700005223732471
Offset: 0
Keywords
Examples
At n=4, a(4) = [x^4] (1 + x*(1+x)^3 )^5 = 250, since (1 + x*(1+x)^3 )^5 = 1 + 5*x + 25*x^2 + 85*x^3 + 250*x^4 +...
Programs
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PARI
a(n)=sum(k=0,n+1,binomial(n+1,k)*binomial((n-1)*k,n-k))
Formula
a(n) = Sum_{k=0..n+1} C(n+1,k) * C((n-1)*k,n-k).
Comments