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

0,3

Links

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

Index entries for reversions of series

Formula

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

Prog

(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);

Crossrefs

Cf. A213644, A370927.

Sequence in context: A317030 A192549 A303001 * A137341 A295899 A291060

Adjacent sequences: A370925 A370926 A370927 * A370929 A370930 A370931

Keyword

nonn

Author

Seiichi Manyama, Mar 06 2024

Status

approved