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

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

Cf. A052830, A367878, A367879.

Cf. A375683.

Sequence in context: A371613 A254382 A354610 * A067848 A269067 A370201

Adjacent sequences: A375681 A375682 A375683 * A375685 A375686 A375687

Keyword

sign

Author

Seiichi Manyama, Aug 24 2024

Status

approved