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

Author

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

Keywords

• easy
• nonn

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..200
• INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 724

Crossrefs

Column k=5 of A225479.

Cf. A000482, A052517.

Programs

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 *)

PARI

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

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

Extensions

Definition clarified by Harvey P. Dale, Oct 14 2019

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