A052724 A simple context-free grammar in a labeled universe.

0, 0, 0, 0, 24, 240, 2160, 30240, 524160, 9434880, 188697600, 4311014400, 108254361600, 2939153817600, 86568043161600, 2753962219008000, 93838712647680000, 3409619685728256000, 131735241369059328000

Offset

0,5

Links

Table of n, a(n) for n=0..18.

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 680

Formula

E.g.f.: (1/2)/x^2*(1-x-(1-2*x+x^2-4*x^3)^(1/2))-(1/2)/x*(1-x-(1-2*x+x^2-4*x^3)^(1/2))-x

Recurrence: {a(1)=0, a(2)=0, a(3)=0, a(4)=24, a(6)=2160, a(7)=30240, (38*n^4+120*n^3-48-4*n+130*n^2+4*n^5)*a(n) +(-193*n^2-52*n^3-302*n-5*n^4-168)*a(n+1) +(96+29*n^2+92*n+3*n^3)*a(n+2) +(-52-3*n^2-25*n)*a(n+3) +(n+6)*a(n+4)=0, a(5)=240}

a(n) = n!*A052702(n). - R. J. Mathar, Oct 18 2013

Maple

spec := [S, {B=Prod(Z, C), C=Union(B, S, Z), S=Prod(B, B)}, labeled]: seq(combstruct[count](spec, size=n), n=0..20);
seq(n!*add(binomial(n-k-2, 2*k-1)*binomial(2*k, k)/(k+1), k=0..n-2), n=0..20);  # Mark van Hoeij, May 12 2013

Crossrefs

Sequence in context: A353358 A353119 A052520 * A357242 A000536 A151720

Adjacent sequences: A052721 A052722 A052723 * A052725 A052726 A052727

Keyword

easy,nonn

Author

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

Status

approved