A377830 Expansion of e.g.f. (1/x) * Series_Reversion( x * exp(-x)/(1 + x)^3 ).

1, 4, 45, 886, 25397, 963216, 45615553, 2595412240, 172624541769, 13150155923200, 1129371806449301, 107987110491257856, 11379014255782146685, 1310277285293012678656, 163703077517048727256425, 22057132253723442887059456, 3188342874266180285119069457, 492178313447920665621400780800

Offset

0,2

Links

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

Index entries for reversions of series

Formula

E.g.f. A(x) satisfies A(x) = (1 + x*A(x))^3 * exp(x * A(x)).

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

Prog

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

Crossrefs

Cf. A088690, A377829.

Sequence in context: A214400 A360344 A197989 * A379700 A380829 A338456

Adjacent sequences: A377827 A377828 A377829 * A377831 A377832 A377833

Keyword

nonn

Author

Seiichi Manyama, Nov 09 2024

Status

approved