A363819 G.f. satisfies A(x) = (1 + x/A(x)^2)/(1 - x)^3.
1, 4, 1, 38, -193, 1697, -14298, 127836, -1175835, 11078851, -106354266, 1036575329, -10230191020, 102031153812, -1026763493315, 10412602349343, -106308046392516, 1091783632303656, -11271378486953873, 116907289944782853, -1217649336037820058
Offset: 0
Keywords
Programs
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PARI
a(n) = (-1)^(n-1)*sum(k=0, n, binomial(3*k-1, k)*binomial(3*(2*k-1), n-k)/(3*k-1));
Formula
a(n) = (-1)^(n-1) * Sum_{k=0..n} binomial(3*k-1,k) * binomial(3*(2*k-1),n-k)/(3*k-1).