A291979 a(n) = (-1)^n*n!*[x^n] exp(-x)/(1 + log(1+x)).

1, 2, 6, 27, 167, 1310, 12394, 137053, 1733325, 24670114, 390204086, 6789564639, 128884276179, 2650516064222, 58701784670138, 1392959655437473, 35257885037803417, 948208649740610466, 27000743345935785670, 811575543670852269347, 25677856392014665436799

Offset

0,2

Comments

Row sums of A291978.

Links

Seiichi Manyama, Table of n, a(n) for n = 0..418

Formula

a(n) ~ sqrt(2*Pi) * n^(n+1/2) * exp(1 - exp(-1)) / (exp(1)-1)^(n+1). - Vaclav Kotesovec, Sep 18 2017

a(n) = 1 + Sum_{k=0..n-1} binomial(n,k) * (n-k-1)! * a(k). - Ilya Gutkovskiy, Apr 26 2021

Maple

a_list := proc(n) exp(-x)/(1 + log(1+x)): series(%, x, n+1):
seq((-1)^k*k!*coeff(%, x, k), k=0..n) end: a_list(20);

Mathematica

nmax = 20; CoefficientList[Series[E^(-x)/(1 + Log[1+x]), {x, 0, nmax}], x] * Range[0, nmax]! * (-1)^Range[0, nmax] (* Vaclav Kotesovec, Sep 18 2017 *)

Prog

(PARI) N=20; x='x+O('x^N); Vec(serlaplace(exp(x)/(1+log(1-x)))) \\ Seiichi Manyama, Oct 20 2021

Crossrefs

Cf. A291978, A343707, A343709, A343710.

Sequence in context: A352139 A234568 A231934 * A070076 A227222 A370982

Adjacent sequences: A291976 A291977 A291978 * A291980 A291981 A291982

Keyword

nonn

Author

Peter Luschny, Sep 16 2017

Status

approved