A052742 A simple context-free grammar in a labeled universe.

0, 0, 2, 12, 144, 2640, 64800, 1985760, 72817920, 3105527040, 150907276800, 8226772646400, 497068582348800, 32962398345676800, 2379770152465305600, 185792734381782528000, 15595576381312671744000, 1400555897449216155648000, 133983477830143785811968000, 13602115002476999012990976000

Offset

0,3

Links

Table of n, a(n) for n=0..19.

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 698

Formula

E.g.f.: (1/2-1/2*x-1/2*(1-6*x+x^2)^(1/2))*x

Recurrence: {a(1)=0, a(2)=2, a(3)=12, (-4*n+n^2-4+n^3)*a(n) +(-6*n^2+6-9*n)*a(n+1) +(n+1)*a(n+2) =0.

a(n) ~ sqrt(3/sqrt(2)-2)*n^(n-1)*(3+2*sqrt(2))^(n-1)/exp(n). - Vaclav Kotesovec, Oct 05 2013

a(n) = n!*A006318(n-2). - R. J. Mathar, Oct 18 2013

Maple

spec := [S, {B=Prod(C, C), C=Union(B, S, Z), S=Prod(Z, C)}, labeled]: seq(combstruct[count](spec, size=n), n=0..20); # end of program
0, 0, seq(simplify(2*n!*hypergeom([ 3-n, n], [2], -1)), n=2..20);  # Mark van Hoeij, May 29 2013

Mathematica

CoefficientList[Series[(1/2-1/2*x-1/2*(1-6*x+x^2)^(1/2))*x, {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Oct 05 2013 *)

Prog

(PARI) x='x+O('x^66); concat([0, 0], Vec( serlaplace( (1/2-1/2*x-1/2*(1-6*x+x^2)^(1/2))*x))) \\ Joerg Arndt, May 29 2013

Crossrefs

Sequence in context: A052740 A227462 A262241 * A035049 A010790 A321631

Adjacent sequences: A052739 A052740 A052741 * A052743 A052744 A052745

Keyword

easy,nonn

Author

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

Status

approved