A052740 A simple context-free grammar in a labeled universe.

0, 1, 2, 12, 144, 2400, 50400, 1290240, 39070080, 1365154560, 54047347200, 2391175987200, 116918542540800, 6260970517401600, 364413626331955200, 22906448213096448000, 1546480919558615040000, 111605770820457897984000

Offset: 0

Author

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

Keywords

• easy
• nonn

Links

• INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 696

Programs

Maple

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

Formula

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

D-finite Recurrence: {a(1)=1, a(0)=0, a(2)=2, a(3)=12, (576*n-9216*n^3-2688*n^2+192-6144*n^4)*a(n) +(-6400*n^3-23112-36480*n^2-54608*n)*a(n+1) +(13184*n+17772+896*n^2)*a(n+2) +(-14800-5176*n)*a(n+3) +1147*a(n+4) =0,.

a(n) = n!*A049140(n). - R. J. Mathar, Oct 18 2013