A370878 Expansion of e.g.f. (1/x) * Series_Reversion( x/(x + exp(x^3/6)) ).

1, 1, 2, 7, 40, 320, 3190, 37870, 526400, 8434720, 153092800, 3099958400, 69237737800, 1691184094600, 44855672061200, 1283910696468400, 39445370739174400, 1294688750568012800, 45213628130719048000, 1673957726914620347200, 65493419262155812928000

Offset: 0

Author

Seiichi Manyama, Mar 03 2024

Keywords

• nonn

Links

• Index entries for reversions of series

Crossrefs

Cf. A352410, A370877.

Programs

PARI

my(N=30, x='x+O('x^N)); Vec(serlaplace(serreverse(x/(x+exp(x^3/6)))/x))

PARI

a(n) = n!*sum(k=0, n\3, (3*k+1)^(k-1)*binomial(n, 3*k)/(6^k*k!));

Formula

a(n) = n! * Sum_{k=0..floor(n/3)} (3*k+1)^(k-1) * binomial(n,3*k)/(6^k * k!).