A052603 E.g.f. (1-x)^3/(1-4x+3x^2-x^3).

1, 1, 8, 78, 984, 15480, 292320, 6441120, 162207360, 4595512320, 144662112000, 5009199148800, 189221439052800, 7743449813299200, 341258374762905600, 16113703632009984000, 811588993992032256000, 43431603596770701312000

Offset: 0

Author

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

Keywords

• easy
• nonn

Links

• INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 548

Programs

Maple

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

Formula

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

Recurrence: {a(1)=1, a(0)=1, a(2)=8, (-11*n-6-n^3-6*n^2)*a(n)+(18+3*n^2+15*n)*a(n+1)+(-4*n-12)*a(n+2)+a(n+3)=0, a(3)=78}

Sum(-1/31*(5*_alpha+3*_alpha^2-6)*_alpha^(-1-n), _alpha=RootOf(-1+4*_Z-3*_Z^2+_Z^3))*n!

a(n)=n!*A052529(n). - R. J. Mathar, Jun 03 2022