A009198 -id:A009198 - cp's OEIS frontend

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

Ilya Gutkovskiy, Jan 18 2018

nonn

Exponential transform of A002741.

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

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

Cf. A002741, A007116, A009198, A191365.

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

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

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

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

A007116 Expansion of e.g.f. (1+x)^(exp(x)).

Original entry on oeis.org

1, 1, 2, 6, 18, 75, 295, 1575, 7196, 48993, 230413, 2164767, 8055938, 139431149, 70125991, 14201296057, -77573062280, 2389977322593, -28817693086263, 615493949444827, -10403976760589602, 215611836994976237

Offset: 0

Simon Plouffe

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Seiichi Manyama, Table of n, a(n) for n = 0..451

Cf. A002741, A009198, A191365.

With[{nn=25},CoefficientList[Series[(1+x)^Exp[x],{x,0,nn}], x] Range[ 0,nn]!] (* Harvey P. Dale, Sep 21 2011 *)

a(n):=sum(sum(binomial(n,i)*k^i*stirling1(n-i,k),i,0,n-k),k,1,n); /* Vladimir Kruchinin, Jun 01 2011 */

a(n) = sum(k=1..n, sum(i=0..n-k, binomial(n,i)*k^i*Stirling1(n-i,k))), n>0, a(0)=1. - Vladimir Kruchinin, Jun 01 2011

|a(n)| ~ n!/(Gamma(-exp(-1))*n^(1+exp(-1))). - Vaclav Kotesovec, Jun 27 2013

Definition and terms corrected, and more terms added by Joerg Arndt, Jun 01 2011

cp's OEIS Frontend

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

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Maple

Mathematica

PARI

Formula