%I #20 Jul 27 2020 16:45:14
%S 0,0,0,0,0,120,1800,21000,235200,2693880,32319000,410031600,
%T 5519487600,78864820320,1194924450720,19166592681600,324817601472000,
%U 5803921108010880,109115988701293440,2154085473710580480,44566174481427360000,964537418717406213120,21799797542483649131520
%N Expansion of e.g.f.: -(log(1-x))^5.
%H Andrew Howroyd, <a href="/A052767/b052767.txt">Table of n, a(n) for n = 0..200</a>
%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=724">Encyclopedia of Combinatorial Structures 724</a>
%F E.g.f.: log(-1/(-1+x))^5.
%F 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.
%F a(n) = 120*A000482(n) = 5!*Stirling1(n,5)*(-1)^(n+1). - _Andrew Howroyd_, Jul 27 2020
%p spec := [S,{B=Cycle(Z),S=Prod(B,B,B,B,B)},labeled]: seq(combstruct[count](spec,size=n), n=0..20);
%t With[{nn=20},CoefficientList[Series[-(Log[1-x])^5,{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, Oct 14 2019 *)
%o (PARI) a(n) = {5!*stirling(n,5,1)*(-1)^(n+1)} \\ _Andrew Howroyd_, Jul 27 2020
%Y Column k=5 of A225479.
%Y Cf. A000482, A052517.
%K easy,nonn
%O 0,6
%A encyclopedia(AT)pommard.inria.fr, Jan 25 2000
%E Definition clarified by _Harvey P. Dale_, Oct 14 2019
%E Terms a(20) and beyond from _Andrew Howroyd_, Jul 27 2020