A052577 a(n) = (3^(n+1)-1)*n!/2.

1, 4, 26, 240, 2904, 43680, 786960, 16531200, 396789120, 10713669120, 321413702400, 10606692096000, 381841394457600, 14891820610867200, 625456552834713600, 28145546185236480000, 1350986237814140928000, 68900298484208615424000, 3720616124549638938624000

Offset: 0

Author

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

Keywords

• easy
• nonn

Links

• INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 520

Programs

Maple

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

Formula

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

Recurrence: {a(0)=1, a(1)=4, (3*n^2+9*n+6)*a(n)+(-4*n-8)*a(n+1)+a(n+2)=0.}.

a(n) = (-1/2+1/2*3^(n+1))*n!.

a(n)=n!*A003462(n+1). - R. J. Mathar, Jun 03 2022