A052738 A simple context-free grammar in a labeled universe.

0, 0, 2, 12, 120, 1920, 40320, 1028160, 30965760, 1077753600, 42551308800, 1878484608000, 91686654259200, 4902558383923200, 284994551761920000, 17895345882365952000, 1207064057173438464000, 87041570211234422784000

Offset: 0

Author

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

Keywords

• easy
• nonn

Links

• INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 694

Programs

Maple

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

Formula

E.g.f.: RootOf(-_Z+_Z^4+_Z^2+x)^2

Recurrence: a(1)=0; a(2)=2; a(3)=12; (9216*n^3-2496*n-576+1152*n^2+6144*n^4)*a(n) +(-9096-30320*n-28032*n^2-7936*n^3)*a(n+1) +(15488*n+6272*n^2+10404)*a(n+2) +(-3784*n-7600)*a(n+3) +589*a(n+4)=0; a(4)=120.

a(n) = n!*A052708(n). - R. J. Mathar, Oct 16 2013