A052767 Expansion of e.g.f.: -(log(1-x))^5.

0, 0, 0, 0, 0, 120, 1800, 21000, 235200, 2693880, 32319000, 410031600, 5519487600, 78864820320, 1194924450720, 19166592681600, 324817601472000, 5803921108010880, 109115988701293440, 2154085473710580480, 44566174481427360000, 964537418717406213120, 21799797542483649131520

Offset

0,6

Links

Andrew Howroyd, Table of n, a(n) for n = 0..200

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 724

Formula

E.g.f.: log(-1/(-1+x))^5.

Recurrence: a(1)=0, a(0)=0, a(2)=0, a(4)=0, a(3)=0, (-1-5*n-10*n^2-10*n^3-5*n^4-n^5)*a(n+1) + (31+5*n^4+70*n^2+30*n^3+75*n)*a(n+2) + (-125*n-90-60*n^2-10*n^3)*a(n+3) + (10*n^2+65+50*n)*a(n+4) + (-15-5*n)*a(n+5) + a(n+6)=0, a(5)=120.

a(n) = 120*A000482(n) = 5!*Stirling1(n,5)*(-1)^(n+1). - Andrew Howroyd, Jul 27 2020

Maple

spec := [S, {B=Cycle(Z), S=Prod(B, B, B, B, B)}, labeled]: seq(combstruct[count](spec, size=n), n=0..20);

Mathematica

With[{nn=20}, CoefficientList[Series[-(Log[1-x])^5, {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Oct 14 2019 *)

Prog

(PARI) a(n) = {5!*stirling(n, 5, 1)*(-1)^(n+1)} \\ Andrew Howroyd, Jul 27 2020

Crossrefs

Column k=5 of A225479.

Cf. A000482, A052517.

Sequence in context: A001118 A354230 A354232 * A353404 A353200 A110839

Adjacent sequences: A052764 A052765 A052766 * A052768 A052769 A052770

Keyword

easy,nonn

Author

encyclopedia(AT)pommard.inria.fr, Jan 25 2000

Extensions

Definition clarified by Harvey P. Dale, Oct 14 2019

Terms a(20) and beyond from Andrew Howroyd, Jul 27 2020

Status

approved