OFFSET
0,4
FORMULA
a(0) = 1; a(n) = -Sum_{k=2..n} binomial(n,k) * (k-1)! * a(n-k).
a(n) ~ -n! / (n * log(n)^2) * (1 - 2*gamma/log(n) + (3*gamma^2 - Pi^2/2)/log(n)^2), where gamma is the Euler-Mascheroni constant A001620. - Vaclav Kotesovec, Oct 29 2020
MATHEMATICA
nmax = 23; CoefficientList[Series[1/(1 - x - Log[1 - x]), {x, 0, nmax}], x] Range[0, nmax]!
a[0] = 1; a[n_] := a[n] = -Sum[Binomial[n, k] (k - 1)! a[n - k], {k, 2, n}]; Table[a[n], {n, 0, 23}]
PROG
(PARI) my(x='x + O('x^30)); Vec(serlaplace(1/(1 - x - log(1 - x)))) \\ Michel Marcus, Oct 29 2020
CROSSREFS
KEYWORD
sign
AUTHOR
Ilya Gutkovskiy, Oct 28 2020
STATUS
approved