A319364 Expansion of e.g.f. exp(x^3/3)/(1 - x).

1, 1, 2, 8, 32, 160, 1000, 7000, 56000, 506240, 5062400, 55686400, 668483200, 8690281600, 121663942400, 1825003980800, 29200063692800, 496401082777600, 8935231687782400, 169769402067865600, 3395388041357312000, 71303153503662080000, 1568669377080565760000, 36079395672853012480000

Offset: 0

Author

Ilya Gutkovskiy, Sep 17 2018

Keywords

• nonn

Links

• Robert Israel, Table of n, a(n) for n = 0..449

Crossrefs

Cf. A000090, A000522, A030977, A052502, A130905, A319365.

Programs

Maple

seq(n!*coeff(series(exp(x^3/3)/(1 - x),x=0,24),x,n),n=0..23); # Paolo P. Lava, Jan 09 2019

Mathematica

nmax = 23; CoefficientList[Series[Exp[x^3/3]/(1 - x), {x, 0, nmax}], x] Range[0, nmax]!

PARI

my(x='x+O('x^30)); Vec(serlaplace(exp(x^3/3)/(1 - x))) \\ Michel Marcus, Dec 17 2020

Formula

a(n) ~ n!*exp(1/3).

D-finite with recurrence: n*a(n) - n^2*a(n-1) - n*(n-1)*(n-2)*a(n-3) + n*(n-1)*(n-2)*(n-3)*a(n-4) = 0. - Robert Israel, Dec 17 2020