A370185 Coefficient of x^n in the expansion of (1+x+x^3)^(2*n).
1, 2, 6, 26, 126, 612, 2970, 14534, 71838, 357884, 1793296, 9026976, 45612450, 231224060, 1175422590, 5989693176, 30586693182, 156483812892, 801908994852, 4115509738188, 21149522157816, 108817959549416, 560500440662872, 2889915938877078, 14913928051929426
Offset: 0
Keywords
Programs
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PARI
a(n, s=3, t=2, 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/3)} binomial(2*n,k) * binomial(2*n-k,n-3*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^3)^2 ). See A369483.