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A298374 Expansion of e.g.f. 1/(1 - x)^exp(-x). 5

%I #14 May 03 2022 10:59:41

%S 1,1,0,0,6,15,65,595,4004,32865,322307,3316511,37845214,471644173,

%T 6319617369,91114344217,1404670896264,23050054222177,401305630237239,

%U 7387282161642715,143360257370842146,2925289119525173741,62612350725688075941,1402681525332544374325

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

%C Exponential transform of A002741.

%H Seiichi Manyama, <a href="/A298374/b298374.txt">Table of n, a(n) for n = 0..450</a>

%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>

%H <a href="/index/Lo#logarithmic">Index entries for sequences related to logarithmic numbers</a>

%F a(n) ~ n! * n^(exp(-1)-1) / Gamma(exp(-1)). - _Vaclav Kotesovec_, May 04 2018

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

%p 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

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

%o (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1-x)^exp(-x))) \\ _Seiichi Manyama_, May 03 2022

%Y Cf. A002741, A007116, A009198, A191365.

%K nonn

%O 0,5

%A _Ilya Gutkovskiy_, Jan 18 2018

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Last modified March 29 11:45 EDT 2024. Contains 371278 sequences. (Running on oeis4.)