A052733 E.g.f.: x^2*(1-sqrt(1-4*x))/2.

0, 0, 0, 6, 24, 240, 3600, 70560, 1693440, 47900160, 1556755200, 57081024000, 2328905779200, 104589041356800, 5124863026483200, 272011960636416000, 15543540607795200000, 951264685197066240000, 62070020709108572160000

Offset

0,4

Comments

Apart from a(3), the same as A052732. - R. J. Mathar, Oct 16 2013

Links

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

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 689

Formula

D-finite with recurrence: a(1)=0; a(2)=0; a(3)=6; a(4)=24; -2*(n+1)*(2*n-5)*a(n)+(n-1)*a(n+1) =0.

a(n) = n!*A000108(n-3). - R. J. Mathar, Oct 16 2013

G.f.: x^2*(1- 2F0(-1/2,3;;4*x)). - R. J. Mathar, Jan 25 2020

Maple

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

Prog

(MuPAD) combinat::catalan(n)*(n+3)! $ n = 0..15; // Zerinvary Lajos, Feb 15 2007

Crossrefs

Sequence in context: A112675 A052583 A052671 * A323449 A010567 A097171

Adjacent sequences: A052730 A052731 A052732 * A052734 A052735 A052736

Keyword

easy,nonn

Author

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

Status

approved