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
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