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A052770 Expansion of e.g.f. log(-1/(-1+x))^4*x.

%I A052770 #14 Jan 13 2025 07:50:51
%S A052770 0,0,0,0,0,120,1440,14280,141120,1462104,16148160,191051520,
%T A052770 2421936000,32840519712,475109002368,7312951114560,119419875993600,
%U A052770 2063254247160192,37617587514390528,721991172931734528
%N A052770 Expansion of e.g.f. log(-1/(-1+x))^4*x.
%H A052770 INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=727">Encyclopedia of Combinatorial Structures 727</a>
%F A052770 Recurrence: {a(1)=0, a(2)=0, a(4)=0, a(3)=0, (n^8+6*n^7-46*n-21*n^2-5*n^4-34*n^5+24+74*n^3+n^6)*a(n) + (-4*n^7+49*n^3-70*n^2+25*n^4-54*n^5-30*n^6+24*n)*a(n+1) + (115*n^4+48*n^5+6*n^6+19*n^2+12*n+80*n^3)*a(n+2) + (-16*n-70*n^3-60*n^2-30*n^4-4*n^5)*a(n+3) + (n^4+6*n^3+11*n^2+6*n)*a(n+4), a(5)=120}.
%p A052770 spec := [S,{B=Cycle(Z),S=Prod(Z,B,B,B,B)},labeled]: seq(combstruct[count](spec,size=n), n=0..20);
%p A052770 # alternative
%p A052770 A052770 := proc(n)
%p A052770         egf := log(-1/(-1+x))^4*x ;
%p A052770         coeftayl(%,x=0,n)*n! ;
%p A052770 end proc:
%p A052770 seq(A052770(n),n=0..20) ; # _R. J. Mathar_, Jan 13 2025
%Y A052770 Cf. A052758, A052783.
%K A052770 easy,nonn
%O A052770 0,6
%A A052770 encyclopedia(AT)pommard.inria.fr, Jan 25 2000