A052629 Expansion of e.g.f. (1-x)/(1-5x+3x^2).

1, 4, 34, 438, 7536, 162120, 4185360, 126060480, 4339278720, 168038478720, 7230318681600, 342214829510400, 17669683572710400, 988372892015308800, 59538455210371737600, 3842709218808235776000, 264549049753191211008000

Offset: 0

Author

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

Keywords

• easy
• nonn

Links

• INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 575 [broken link].

Crossrefs

Cf. A018902.

Programs

Maple

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

Formula

E.g.f.: -(-1+x)/(1-5*x+3*x^2).

Recurrence: a(0)=1, a(1)=4, (3*n^2+9*n+6)*a(n) +(-10-5*n)*a(n+1) +a(n+2)=0.

Sum(-1/13*(-3+_alpha)*_alpha^(-1-n), _alpha=RootOf(1-5*_Z+3*_Z^2))*n!

a(n) = n!*A018902(n). - R. J. Mathar, Jun 03 2022