A370926 Expansion of e.g.f. (1/x) * Series_Reversion( x/(1 + x*exp(x^3/6)) ).

1, 1, 2, 6, 28, 220, 2520, 34510, 519680, 8527680, 154831600, 3151456000, 71830281600, 1809141934600, 49559087177600, 1459865188782000, 45970426027926400, 1543274016213529600, 55120521154277779200, 2088917638216953544000, 83717918489664018560000

Offset: 0

Author

Seiichi Manyama, Mar 05 2024

Keywords

• nonn

Links

• Index entries for reversions of series

Crossrefs

Cf. A161633, A370889.

Cf. A365287.

Programs

PARI

my(N=30, x='x+O('x^N)); Vec(serlaplace(serreverse(x/(1+x*exp(x^3/6)))/x))

PARI

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

Formula

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