A372369 Coefficient of x^n in the expansion of ( (1+x+x^2)^3 / (1+x) )^n.
1, 2, 12, 65, 388, 2352, 14565, 91289, 577764, 3683459, 23621462, 152203482, 984598741, 6390596591, 41596873869, 271424778015, 1774892605284, 11628321367815, 76311803660025, 501554760288813, 3300889231760238, 21750690436059188, 143481522241226962
Offset: 0
Keywords
Programs
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PARI
a(n, s=2, t=3, u=-1) = 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(2*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) / (1+x+x^2)^3 ).