A052741 A simple context-free grammar in a labeled universe.

0, 0, 0, 0, 24, 360, 6480, 141120, 3628800, 107775360, 3632428800, 136994457600, 5716405094400, 261472603392000, 13009267682611200, 699459327350784000, 40413205580267520000, 2497069798642298880000

Offset

0,5

Links

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

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 697

Formula

E.g.f.: (1/2-x-1/2*(1-4*x)^(1/2))*(1/2-1/2*(1-4*x)^(1/2))*x

Recurrence: {a(1)=0, a(2)=0, a(3)=0, a(4)=24, a(5)=360, (-22*n+2*n^2-20+4*n^3)*a(n) +(-5*n^2+6-7*n)*a(n+1) +(n+1)*a(n+2) =0.

a(n) = n!*A000245(n-3). - R. J. Mathar, Oct 18 2013

Maple

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

Crossrefs

Sequence in context: A309843 A081144 A126780 * A046905 A028115 A125481

Adjacent sequences: A052738 A052739 A052740 * A052742 A052743 A052744

Keyword

easy,nonn

Author

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

Status

approved