A052608 E.g.f. (1-x)/(1-2x-x^2).

1, 1, 6, 42, 408, 4920, 71280, 1204560, 23264640, 505491840, 12203654400, 324084499200, 9388910361600, 294668851276800, 9959509521561600, 360665744414976000, 13931586106454016000, 571775010100310016000

Offset

0,3

Links

Table of n, a(n) for n=0..17.

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 553

Formula

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

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

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

a(n) = n!*A001333(n). - R. J. Mathar, Jun 03 2022

Maple

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

Mathematica

Table[LucasL[n, 2]*n!/2, {n, 0, 17}] (* Zerinvary Lajos, Jul 09 2009 *)
With[{nn=20}, CoefficientList[Series[(1-x)/(1-2x-x^2), {x, 0, nn}], x] Range[ 0, nn]!] (* Harvey P. Dale, Jul 01 2017 *)

Crossrefs

Sequence in context: A225497 A336950 A304071 * A245248 A197712 A306173

Adjacent sequences: A052605 A052606 A052607 * A052609 A052610 A052611

Keyword

easy,nonn

Author

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

Status

approved