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A352147
Expansion of e.g.f. 1/(exp(x) + log(1 + x)).
5
1, -2, 8, -51, 437, -4685, 60299, -905583, 15543989, -300163717, 6440430159, -152007707357, 3913861488767, -109171084473763, 3279401359094041, -105546729767585411, 3623462164916028569, -132169615185372857001, 5104616345453966073403
OFFSET
0,2
LINKS
FORMULA
a(0) = 1; a(n) = Sum_{k=1..n} ((-1)^k * (k-1)! - 1) * binomial(n,k) * a(n-k).
MATHEMATICA
m = 18; Range[0, m]! * CoefficientList[Series[1/(Exp[x] + Log[1 + x]), {x, 0, m}], x] (* Amiram Eldar, Mar 06 2022 *)
PROG
(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(exp(x)+log(1+x))))
(PARI) a(n) = if(n==0, 1, sum(k=1, n, ((-1)^k*(k-1)!-1)*binomial(n, k)*a(n-k)));
CROSSREFS
KEYWORD
sign
AUTHOR
Seiichi Manyama, Mar 06 2022
STATUS
approved