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URL: https://oeis.org/A291979

⇱ A291979 - OEIS

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A291979
a(n) = (-1)^n*n!*[x^n] exp(-x)/(1 + log(1+x)).
12
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
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
a(n) = Sum_{k=0..n} Sum_{j=0..k} binomial(n,k)*j!*A132393(k,j). - Fabian Pereyra, Aug 29 2024
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
KEYWORD
nonn
AUTHOR
Peter Luschny, Sep 16 2017
STATUS
approved