A364620 G.f. satisfies A(x) = 1/(1-x)^2 + x*A(x)^3.
1, 3, 12, 67, 449, 3315, 25963, 211685, 1777410, 15263446, 133427406, 1183336278, 10620959908, 96292118665, 880540044576, 8112042293581, 75218203558241, 701439747294225, 6574348389693202, 61897799517155325, 585138783209680944, 5551797662571097495
Offset: 0
Keywords
Programs
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PARI
a(n) = sum(k=0, n, binomial(n+3*k+1, 4*k+1)*binomial(3*k, k)/(2*k+1));
Formula
a(n) = Sum_{k=0..n} binomial(n+3*k+1,4*k+1) * binomial(3*k,k) / (2*k+1).