A362085 a(n) = Sum_{k=0..n} (-1)^k * binomial(-3,k) * binomial(n*k,n-k).
1, 3, 12, 55, 315, 2106, 15946, 134730, 1253637, 12702961, 138955146, 1629581955, 20371061009, 270124999977, 3783651174906, 55780472480036, 862795543656489, 13963065117796548, 235845816764772718, 4148499020022749151, 75841424406989195136
Offset: 0
Keywords
Links
- Seiichi Manyama, Table of n, a(n) for n = 0..492
Programs
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PARI
a(n) = sum(k=0, n, binomial(k+2, k)*binomial(n*k, n-k));
Formula
a(n) = Sum_{k=0..n} binomial(k+2,k) * binomial(n*k,n-k).
a(n) = [x^n] 1/(1 - x*(1+x)^n)^3.