A381829 G.f. A(x) satisfies A(x) = C(x*A(x)) / (1 - x*A(x)^3), where C(x) is the g.f. of A000108.
1, 2, 12, 97, 905, 9187, 98578, 1099980, 12636101, 148449436, 1775331503, 21541303494, 264533752068, 3281596216087, 41062196808517, 517655936768189, 6568539787903369, 83827401412072474, 1075254139150601581, 13855040994605807348, 179256835556387995412, 2327788724156294034612
Offset: 0
Keywords
Programs
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PARI
a(n) = sum(k=0, n, binomial(3*n+1, k)*binomial(4*n-3*k, n-k))/(3*n+1);
Formula
a(n) = (1/(3*n+1)) * Sum_{k=0..n} binomial(3*n+1,k) * binomial(4*n-3*k,n-k).