A052725 A simple context-free grammar in a labeled universe.
0, 0, 0, 0, 24, 480, 10080, 262080, 8104320, 287400960, 11496038400, 512691379200, 25231888281600, 1358412133478400, 79419074570035200, 5011102330730496000, 339416862385176576000, 24564200609223475200000
Offset: 0
Links
- INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 681
Programs
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Maple
spec := [S,{B=Prod(C,C),C=Union(B,S,Z),S=Prod(B,B)},labeled]: seq(combstruct[count](spec,size=n), n=0..20);
Formula
E.g.f.: RootOf(-_Z+_Z^4+_Z^2+x)-RootOf(-_Z+_Z^4+_Z^2+x)^2-x
D-finite Recurrence: {a(1)=0, a(2)=0, a(3)=0, a(4)=24, a(5)=480, a(6)=10080, (-32256*n^3+85248*n^2-73728*n^5+2304*n-4608-184320*n^4)*a(n) +(-41472*n^3-241344*n^2-92736-289440*n+9216*n^4)*a(n+1) +(-59520*n^2-34048*n^3+79800+56512*n)*a(n+2) +(-7456*n^2-46176*n-61988)*a(n+3) +(-572+2228*n)*a(n+4) +217*a(n+5) =0.
a(n) = n!*A052710(n). - R. J. Mathar, Oct 18 2013