A375684 - OEIS

A375684

Expansion of e.g.f. 1 / (1 - x * log(1 - x)).

1, 0, -2, -3, 16, 90, -204, -4200, -5312, 254016, 1586160, -17970480, -294932736, 790115040, 54224747136, 216483714720, -10481294822400, -137535688281600, 1798183916660736, 58769251106526720, -95282580797291520, -23811620975395061760, -203282679617698222080

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,3

LINKS

Table of n, a(n) for n=0..22.

FORMULA

a(0) = 1; a(n) = -n! * Sum_{k=2..n} 1/(k-1) * a(n-k)/(n-k)!.

a(n) = n! * Sum_{k=0..floor(n/2)} (-1)^k * k! * |Stirling1(n-k,k)|/(n-k)!.

PROG

(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1-x*log(1-x))))

(PARI) a(n) = n!*sum(k=0, n\2, (-1)^k*k!*abs(stirling(n-k, k, 1))/(n-k)!);

CROSSREFS