OFFSET
0,5
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..200
Gottfried Helms, Infinite sum of powerseries likely converges to a powerseries with rational coefficients ... May 14, 2021
Vaclav Kotesovec, Plot of (abs(a(n))/n!)^(1/n) for n = 1..1000
Vladimir Kruchinin and D. V. Kruchinin, Composita and their properties, arXiv:1103.2582 [math.CO], 2011-2013.
FORMULA
a(n) = n! * Sum_{k=1..n} k^(n-k-1) * (-1)^(k+1)/(n-k)!. - Vladimir Kruchinin, Sep 07 2010
a(n) = n - Sum_{k=1..n-1} binomial(n-1,k-1) * (n-k) * a(k). - Ilya Gutkovskiy, Jan 17 2020
Lim sup_{n->infinity} (abs(a(n))/n!)^(1/n) = 1/abs(LambertW(-1)) = 1/A238274. - Vaclav Kotesovec, May 26 2021
MAPLE
a:= n-> n! *add(k^(n-k-1) *(-1)^(k+1) /(n-k)!, k=1..n):
seq(a(n), n=0..25);
MATHEMATICA
With[{nn=30}, CoefficientList[Series[Log[1+Exp[x]x], {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Oct 22 2016 *)
PROG
(PARI) seq(n)=Vec(serlaplace(log(1 + exp(x + O(x^n))*x)), -(n+1)) \\ Andrew Howroyd, May 26 2021
CROSSREFS
KEYWORD
sign,easy
AUTHOR
EXTENSIONS
Extended with signs by Olivier Gérard, Mar 15 1997
Definition clarified by Harvey P. Dale, Oct 22 2016
STATUS
approved