A052729 A simple context-free grammar in a labeled universe.

0, 0, 2, 12, 168, 3120, 75600, 2237760, 78382080, 3169393920, 145297152000, 7446479040000, 421880659200000, 26181558769766400, 1766275594501017600, 128700516232544256000, 10073126652104355840000

Offset: 0

Author

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

Keywords

• easy
• nonn

Links

• INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 685

Programs

Maple

spec := [S,{B=Prod(S,C),S=Prod(C,C),C=Union(B,S,Z)},labeled]: seq(combstruct[count](spec,size=n), n=0..20);
seq(2*add((n+k-1)!/(n-k-2)!/(2*k+2-n)!, k= ceil(n/2)-1..n-2),n=0..20);  # Mark van Hoeij, May 12 2013

Formula

E.g.f.: RootOf(-_Z+_Z^2+_Z^3+x)^2

Recurrence: {a(1)=0, a(2)=2, a(3)=12, (21*n-27*n^3-6)*a(n) +(-49*n^2-6-65*n)*a(n+1) +(-33-17*n)*a(n+2) +5*a(n+3) =0.

a(n) = n!*A052706(n). - R. J. Mathar, Oct 18 2013