A298374 Expansion of e.g.f. 1/(1 - x)^exp(-x).

1, 1, 0, 0, 6, 15, 65, 595, 4004, 32865, 322307, 3316511, 37845214, 471644173, 6319617369, 91114344217, 1404670896264, 23050054222177, 401305630237239, 7387282161642715, 143360257370842146, 2925289119525173741, 62612350725688075941, 1402681525332544374325

Offset: 0

Author

Ilya Gutkovskiy, Jan 18 2018

Keywords

• nonn

Comments

Exponential transform of A002741.

Examples

			1/(1 - x)^exp(-x) = 1 + x/1! + 6*x^4/4! + 15*x^5/5! + 65*x^6/6! + 595*x^7/7! + ...
		

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..450
• N. J. A. Sloane, Transforms
• Index entries for sequences related to logarithmic numbers

Crossrefs

Cf. A002741, A007116, A009198, A191365.

Programs

Maple

a:=series(1/(1-x)^exp(-x),x=0,24): seq(n!*coeff(a,x,n),n=0..23); # Paolo P. Lava, Mar 26 2019

Mathematica

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

PARI

my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1-x)^exp(-x))) \\ Seiichi Manyama, May 03 2022

Formula

a(n) ~ n! * n^(exp(-1)-1) / Gamma(exp(-1)). - Vaclav Kotesovec, May 04 2018