A319364 - OEIS

%I #12 Dec 17 2020 20:30:40

%S 1,1,2,8,32,160,1000,7000,56000,506240,5062400,55686400,668483200,

%T 8690281600,121663942400,1825003980800,29200063692800,496401082777600,

%U 8935231687782400,169769402067865600,3395388041357312000,71303153503662080000,1568669377080565760000,36079395672853012480000

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

%H Robert Israel, <a href="/A319364/b319364.txt">Table of n, a(n) for n = 0..449</a>

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

%F 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

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

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

%o (PARI) my(x='x+O('x^30)); Vec(serlaplace(exp(x^3/3)/(1 - x))) \\ _Michel Marcus_, Dec 17 2020

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

%K nonn

%O 0,3

%A _Ilya Gutkovskiy_, Sep 17 2018