A052730 A simple context-free grammar in a labeled universe.

0, 0, 0, 6, 72, 1440, 35280, 1058400, 37376640, 1520830080, 70053984000, 3603888288000, 204806714112000, 12742502111539200, 861483843034214400, 62887137880799232000, 4929809613351727104000, 413044721987184967680000

Offset: 0

Author

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

Keywords

• easy
• nonn

Links

• INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 686

Programs

Maple

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

Formula

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

D-finite Recurrence: {a(1)=0, a(2)=0, a(3)=6, a(4)=72, (-105*n+135*n^3+30)*a(n) +(-130-107*n+29*n^2)*a(n+1) +(-99-91*n)*a(n+2) +15*a(n+3)=0.

a(n) = n!*A052703(n). - R. J. Mathar, Oct 18 2013