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A375683
Expansion of e.g.f. 1 / (1 + x * (exp(x) - 1)).
1
1, 0, -2, -3, 20, 115, -306, -6307, -6616, 462663, 2956130, -38945951, -656504388, 2325876683, 145820995670, 562691968005, -33452317341616, -449954883966065, 7055017491780810, 233802046526955497, -571834988279277340, -112474674691684827501
OFFSET
0,3
FORMULA
a(0) = 1; a(n) = -n * Sum_{k=2..n} binomial(n-1,k-1) * a(n-k).
a(n) = n! * Sum_{k=0..floor(n/2)} (-1)^k * k! * Stirling2(n-k,k)/(n-k)!.
PROG
(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1+x*(exp(x)-1))))
(PARI) a(n) = n!*sum(k=0, n\2, (-1)^k*k!*stirling(n-k, k, 2)/(n-k)!);
CROSSREFS
KEYWORD
sign
AUTHOR
Seiichi Manyama, Aug 24 2024
STATUS
approved