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

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

Author

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

Keywords

• easy
• nonn

Links

• INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 701

Crossrefs

Cf. A052758, A052770, A052783.

Programs

Magma

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

Maple

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

Mathematica

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

Maxima

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

Formula

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