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A352146
Expansion of e.g.f. 1/(exp(x) + log(1 - x)).
5
1, 0, 0, 1, 5, 23, 139, 1069, 9365, 90971, 981647, 11697167, 152304591, 2149063421, 32668289913, 532328418153, 9256383832665, 171066343532055, 3348245897484091, 69189708307509195, 1505284330388457451, 34391324279752372105, 823258887611521993045
OFFSET
0,5
LINKS
FORMULA
a(0) = 1; a(n) = Sum_{k=1..n} ((k-1)! - 1) * binomial(n,k) * a(n-k).
a(n) ~ n! * (1-r) / ((1 - (1-r)*exp(r)) * r^(n+1)), where r = 0.9183335761894542037857295468680123485973875022318007816308... is the root of the equation exp(r) = -log(1-r). - Vaclav Kotesovec, Mar 06 2022
MATHEMATICA
m = 22; Range[0, m]! * CoefficientList[Series[1/(Exp[x] + Log[1 - x]), {x, 0, m}], x] (* Amiram Eldar, Mar 06 2022 *)
PROG
(PARI) my(N=40, x='x+O('x^N)); Vec(serlaplace(1/(exp(x)+log(1-x))))
(PARI) a(n) = if(n==0, 1, sum(k=1, n, ((k-1)!-1)*binomial(n, k)*a(n-k)));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Mar 06 2022
STATUS
approved