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

%I A052745 #28 Jan 20 2025 06:35:12
%S A052745 0,0,0,6,24,110,600,3836,28224,235224,2191680,22584672,255087360,
%T A052745 3134139840,41620400640,594082771200,9070900715520,147531542054400,
%U A052745 2546434166169600,46489412442009600,895079522340864000,18125736166340812800,385129713617510400000
%N A052745 Expansion of e.g.f. log(-1/(-1+x))^2*x.
%H A052745 INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=701">Encyclopedia of Combinatorial Structures 701</a>
%F A052745 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.
%F A052745 a(n) = (-1)^(n+1)*2*n*Stirling1(n-1, 2). - _Vladeta Jovovic_, Nov 08 2003
%p A052745 spec := [S,{B=Cycle(Z),S=Prod(Z,B,B)},labeled]: seq(combstruct[count](spec,size=n), n=0..20);
%p A052745 # alternative
%p A052745 A052745 := proc(n)
%p A052745     (log(1/(1-x)))^2*x ;
%p A052745     coeftayl(%,x=0,n)*n! ;
%p A052745 end proc:
%p A052745 seq(A052745(n),n=0..20) ; # _R. J. Mathar_, Jan 20 2025
%t A052745 Range[0, 30]! CoefficientList[Series[Log[-1/(-1 + x)]^2 x,{x, 0, 30}], x] (* _Vincenzo Librandi_, Jul 08 2015 *)
%o A052745 (Maxima) makelist((-1)^(n+1)*2*n*stirling1(n-1, 2), n, 0, 20); /* _Bruno Berselli_, May 25 2011 */
%o A052745 (Magma) [0] cat [(-1)^(n+1)*2*n*StirlingFirst(n-1, 2): n in [1..30]]; // _Vincenzo Librandi_, Jul 08 2015
%Y A052745 Cf. A052758, A052770, A052783.
%K A052745 easy,nonn
%O A052745 0,4
%A A052745 encyclopedia(AT)pommard.inria.fr, Jan 25 2000