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

0, 0, 0, 0, 0, 120, 1440, 14280, 141120, 1462104, 16148160, 191051520, 2421936000, 32840519712, 475109002368, 7312951114560, 119419875993600, 2063254247160192, 37617587514390528, 721991172931734528

Offset: 0

Author

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

Keywords

• easy
• nonn

Links

• INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 727

Crossrefs

Cf. A052758, A052783.

Programs

Maple

spec := [S,{B=Cycle(Z),S=Prod(Z,B,B,B,B)},labeled]: seq(combstruct[count](spec,size=n), n=0..20);
# alternative
A052770 := proc(n)
        egf := log(-1/(-1+x))^4*x ;
        coeftayl(%,x=0,n)*n! ;
end proc:
seq(A052770(n),n=0..20) ; # R. J. Mathar, Jan 13 2025

Formula

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}.