A364647 G.f. satisfies A(x) = 1/(1 - 5*x) - x*A(x)^3.
1, 4, 13, 38, 135, 677, 3538, 15868, 63313, 268430, 1348190, 7038185, 33328258, 144159428, 642323050, 3213846836, 16700677289, 80935833050, 363843867265, 1660048399600, 8276473557820, 42830085070355, 210286731046320, 967456811687945, 4476690297795850
Offset: 0
Keywords
Programs
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PARI
a(n) = sum(k=0, n, (-1)^k*5^(n-k)*binomial(n+k, 2*k)*binomial(3*k, k)/(2*k+1));
Formula
a(n) = Sum_{k=0..n} (-1)^k * 5^(n-k) * binomial(n+k,2*k) * binomial(3*k,k) / (2*k+1).