A052605 Expansion of E.g.f. x*(1-x)/(1-x-x^3).

0, 1, 0, 0, 24, 120, 720, 10080, 120960, 1451520, 21772800, 359251200, 6227020800, 118313395200, 2440992153600, 53614649088000, 1255367393280000, 31300493672448000, 825906208038912000

Offset

0,5

Links

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

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 550

Formula

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

Recurrence: a(1)=1, a(0)=0, a(2)=0, (-11*n-6-n^3-6*n^2)*a(n) +(-n-3)*a(n+2) +a(n+3) = 0.

Sum(1/31*(_alpha+11*_alpha^2-3)*_alpha^(-1-n), _alpha=RootOf(-1+_Z+_Z^3))*n!.

a(n)=n!*A078012(n-1). - R. J. Mathar, Jun 03 2022

Maple

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

Crossrefs

Sequence in context: A342856 A293050 A052581 * A195917 A334189 A042120

Adjacent sequences: A052602 A052603 A052604 * A052606 A052607 A052608

Keyword

easy,nonn

Author

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

Status

approved