A052783 -id:A052783 - cp's OEIS frontend

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

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

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 727

Cf. A052758, A052783.

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

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}.

A052745 Expansion of e.g.f. log(-1/(-1+x))^2*x.

Original entry on oeis.org

0, 0, 0, 6, 24, 110, 600, 3836, 28224, 235224, 2191680, 22584672, 255087360, 3134139840, 41620400640, 594082771200, 9070900715520, 147531542054400, 2546434166169600, 46489412442009600, 895079522340864000, 18125736166340812800, 385129713617510400000

Offset: 0

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

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 701

Cf. A052758, A052770, A052783.

[0] cat [(-1)^(n+1)*2*n*StirlingFirst(n-1, 2): n in [1..30]]; // Vincenzo Librandi, Jul 08 2015

spec := [S,{B=Cycle(Z),S=Prod(Z,B,B)},labeled]: seq(combstruct[count](spec,size=n), n=0..20);
# alternative
A052745 := proc(n)
    (log(1/(1-x)))^2*x ;
    coeftayl(%,x=0,n)*n! ;
end proc:
seq(A052745(n),n=0..20) ; # R. J. Mathar, Jan 20 2025

Range[0, 30]! CoefficientList[Series[Log[-1/(-1 + x)]^2 x,{x, 0, 30}], x] (* Vincenzo Librandi, Jul 08 2015 *)

makelist((-1)^(n+1)*2*n*stirling1(n-1, 2), n, 0, 20); /* Bruno Berselli, May 25 2011 */

Recurrence: a(1)=0, a(2)=0, a(3)=6, (-n+n^4+n^3-3*n^2+2)*a(n)+(-2*n^3-3*n^2+2*n)*a(n+1)+(n^2+n)*a(n+2)=0.

a(n) = (-1)^(n+1)*2*n*Stirling1(n-1, 2). - Vladeta Jovovic, Nov 08 2003

cp's OEIS Frontend

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

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