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A052783 Expansion of e.g.f. x*log(-1/(-1+x))^5.

%I A052783 #17 Jan 20 2025 06:38:22
%S A052783 0,0,0,0,0,0,720,12600,168000,2116800,26938800,355509000,4920379200,
%T A052783 71753338800,1104107484480,17923866760800,306665482905600,
%U A052783 5521899225024000,104470579944195840,2073203785324575360
%N A052783 Expansion of e.g.f. x*log(-1/(-1+x))^5.
%H A052783 INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=740">Encyclopedia of Combinatorial Structures 740</a>
%F A052783 Recurrence: {a(1)=0, a(2)=0, a(4)=0, a(3)=0, a(5)=0, a(6)=720, (500*n^3 + 55*n^2 - 300*n^4 - n^10 + 120 - 224*n^5 - 20*n^8 + 146*n^6 - 10*n^9 + 60*n^7 - 326*n)*a(n) + (225*n^7 - n^4 - 299*n^5 + 120*n + 60*n^8 + 5*n^9 + 195*n^6 - 446*n^2 + 501*n^3)*a(n + 1) + ( - 535*n^3 - 895*n^4 - 10*n^8 - 130*n^7 - 300*n^2 - 1135*n^5 - 595*n^6)*a(n + 2) + (130*n^6 + 10*n^7 + 200*n + 1425*n^3 + 1330*n^4 + 615*n^5 + 790*n^2)*a(n + 3) + ( - 150*n - 455*n^2 - 60*n^5 - 5*n^6 - 510*n^3 - 260*n^4)*a(n + 4) + (n^5 + 10*n^4 + 35*n^3 + 50*n^2 + 24*n)*a(n + 5)}.
%p A052783 spec := [S,{B=Cycle(Z),S=Prod(Z,B,B,B,B,B)},labeled]: seq(combstruct[count](spec,size=n), n=0..20);
%p A052783 # alternative
%p A052783 A052783 := proc(n)
%p A052783     (log(1/(1-x)))^5*x ;
%p A052783     coeftayl(%,x=0,n)*n! ;
%p A052783 end proc:
%p A052783 seq(A052783(n),n=0..20) ; # _R. J. Mathar_, Jan 20 2025
%Y A052783 Cf. A052745, A052758, A052770.
%K A052783 easy,nonn
%O A052783 0,7
%A A052783 encyclopedia(AT)pommard.inria.fr, Jan 25 2000