A365032 E.g.f. satisfies A(x) = exp(x * A(x) * (1 + x * A(x))^3).
1, 1, 9, 106, 1949, 47376, 1443757, 53003392, 2278044729, 112267072000, 6242682602321, 386708915902464, 26411820455554261, 1971959747016534016, 159794005364013403125, 13967707431203856449536, 1310083060716906045342833, 131245686122586065682628608
Offset: 0
Keywords
Programs
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PARI
a(n) = n!*sum(k=0, n, (n+1)^(k-1)*binomial(3*k, n-k)/k!);
Formula
a(n) = n! * Sum_{k=0..n} (n+1)^(k-1) * binomial(3*k,n-k)/k!.
E.g.f.: (1/x) * Series_Reversion( x*exp(-x*(1 + x)^3) ). - Seiichi Manyama, Sep 23 2024