A052867 E.g.f.: log(-(-1+x)^2/(-1+2*x)).

0, 0, 2, 12, 84, 720, 7440, 90720, 1280160, 20563200, 370863360, 7424524800, 163419379200, 3923023104000, 102011054745600, 2856483889459200, 85697132032512000, 2742350070620160000, 93240613775941632000

Offset: 0

Author

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

Keywords

• easy
• nonn

Comments

Previous name was: A simple grammar.

Links

• INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 838

Programs

Maple

spec := [S,{B=Sequence(Z,1 <= card),C=Prod(B,B),S= Cycle(C)},labeled]: seq(combstruct[count](spec,size=n), n=0..20);

Mathematica

Range[0,19]! CoefficientList[Series[Log[-(-1 + x)^2/(-1 + 2 x)], {x, 0, 19}], x] (* Vincenzo Librandi, Jul 09 2015 *)

Formula

D-finite with Recurrence: {a(1)=0, a(2)=2, (2*n^2+2*n)*a(n)-3*(n+1)*a(n+1)+a(n+2)}.

a(n) = -2*GAMMA(n+1)+2^(n+1)*GAMMA(n+1).

a(n) = 2*A052589(n-1). - R. J. Mathar, Jun 03 2022