A370170 Coefficient of x^n in the expansion of (1+x+x^2)^(3*n).
1, 3, 21, 156, 1221, 9828, 80580, 669294, 5612805, 47419905, 402993396, 3441242544, 29502452868, 253778827695, 2189249293266, 18932541179706, 164081616775173, 1424741956592535, 12392093363519415, 107946143556797700, 941580123046540596
Offset: 0
Keywords
Links
- Seiichi Manyama, Table of n, a(n) for n = 0..1000
Programs
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PARI
a(n, s=2, t=3, u=0) = sum(k=0, n\s, binomial(t*n, k)*binomial((t+u)*n-k, n-s*k));
Formula
a(n) = Sum_{k=0..floor(n/2)} binomial(3*n,k) * binomial(3*n-k,n-2*k).
The g.f. exp( Sum_{k>=1} a(k) * x^k/k ) has integer coefficients and equals (1/x) * Series_Reversion( x / (1+x+x^2)^3 ). See A365128.