A052876 Expansion of e.g.f. (exp(x)-1)^2/(-2+exp(x))^2.

0, 0, 2, 18, 158, 1530, 16622, 201978, 2724878, 40492890, 657944942, 11611834938, 221291822798, 4530383962650, 99179581033262, 2312402554523898, 57211901491595918, 1497211181084718810

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 847

Crossrefs

Cf. A000670, A069321, A091106.

Programs

Maple

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

Mathematica

With[{nn=20},CoefficientList[Series[((Exp[x]-1)^2/(Exp[x]-2)^2),{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, Jul 19 2018 *)

Formula

E.g.f.: (exp(x)-1)^2/(-2+exp(x))^2.

From Mario Catalani (mario.catalani(AT)unito.it), Dec 22 2003: (Start)

a(n) = A069321(n) - A000670(n).

a(n) = 2*A091106(n)+2. (End)

Extensions

Name changed by Wesley Ivan Hurt, Jun 26 2022