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

0,3

Links

Table of n, a(n) for n=0..17.

Formula

a(n) = n! * Sum_{k=0..n} (n+1)^(k-1) * binomial(3*k,n-k)/k!.

Prog

(PARI) a(n) = n!*sum(k=0, n, (n+1)^(k-1)*binomial(3*k, n-k)/k!);

Crossrefs

Cf. A088695, A365031.

Cf. A364940.

Sequence in context: A357295 A367789 A316145 * A039619 A374071 A249048

Adjacent sequences: A365029 A365030 A365031 * A365033 A365034 A365035

Keyword

nonn

Author

Seiichi Manyama, Aug 17 2023

Status

approved