A370931 Expansion of e.g.f. (1/x) * Series_Reversion( x*(1 - x*exp(x^3/6)) ).

1, 1, 4, 30, 340, 5180, 99360, 2300830, 62473600, 1946941920, 68507714800, 2686816932800, 116225776497600, 5497681373384200, 282305750023897600, 15640212734095950000, 929908726447266966400, 59061538103044360083200, 3990922849835432102592000

Offset: 0

Author

Seiichi Manyama, Mar 06 2024

Keywords

• nonn

Links

• Index entries for reversions of series

Crossrefs

Cf. A213644, A370930.

Cf. A358265.

Programs

PARI

my(N=20, x='x+O('x^N)); Vec(serlaplace(serreverse(x*(1-x*exp(x^3/6)))/x))

PARI

a(n) = sum(k=0, n\3, (n-3*k)^k*(2*n-3*k)!/(6^k*k!*(n-3*k)!))/(n+1);

Formula

a(n) = (1/(n+1)) * Sum_{k=0..floor(n/3)} (n-3*k)^k * (2*n-3*k)!/(6^k * k! * (n-3*k)!).