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

0,5

Links

Table of n, a(n) for n=0..17.

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 681

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

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);

Crossrefs

Sequence in context: A200979 A361576 A052715 * A360517 A006548 A159877

Adjacent sequences: A052722 A052723 A052724 * A052726 A052727 A052728

Keyword

easy,nonn

Author

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

Status

approved