A370928 Expansion of e.g.f. (1/x) * Series_Reversion( x*(1 - x*exp(x^3)) ).

1, 1, 4, 30, 360, 5880, 120960, 2996280, 86889600, 2889976320, 108501724800, 4539844108800, 209497816281600, 10570762445443200, 578997352591257600, 34214810278128480000, 2169772724008976486400, 146984464202544531763200

Offset: 0

Author

Seiichi Manyama, Mar 06 2024

Keywords

• nonn

Links

• Index entries for reversions of series

Crossrefs

Cf. A213644, A370927.

Programs

PARI

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

PARI

a(n) = sum(k=0, n\3, (n-3*k)^k*(2*n-3*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)!/(k! * (n-3*k)!).