A052744 E.g.f. x*(1-2*x-2*x^2-sqrt(1-4*x-4*x^2))/ (2*(1+x)^2).

0, 0, 0, 6, 48, 840, 17280, 448560, 13789440, 491702400, 19929369600, 904873939200, 45486949939200, 2507639957222400, 150419515915468800, 9752720435377920000, 679630757528346624000, 50655177765863903232000

Offset: 0

Author

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

Keywords

• easy
• nonn

Links

• INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 700

Programs

Maple

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

Formula

D-finite with recurrence: a(1)=0, a(2)=0, a(3)=6, (-4*n^4-24*n-24*n^3-44*n^2)*a(n) +(-8*n^3-42*n^2-12-58*n)*a(n+1) +(-3*n^2-8*n+3)*a(n+2) +(n+2)*a(n+3)=0, a(4)=48, a(5)=840, a(6)=17280.

a(n) ~ sqrt(58-41*sqrt(2))*(1+sqrt(2))^(n-1)*2^n*n^(n-1)*exp(-n). - Vaclav Kotesovec, Aug 18 2013

a(n)= n!*A052705(n-1). - R. J. Mathar, Oct 26 2013