A052689 Expansion of e.g.f. (1+x-x^2)/((1-x)*(1-x^2)).

1, 2, 4, 18, 72, 480, 2880, 25200, 201600, 2177280, 21772800, 279417600, 3353011200, 49816166400, 697426329600, 11769069312000, 188305108992000, 3556874280960000, 64023737057280000, 1338096104497152000, 26761922089943040000, 613091306060513280000

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 637

Formula

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

Recurrence: a(0)=1, a(1)=2, a(2)=4, (n+1)*a(n) = n*a(n-1) + (n-1)*n*(n+2)*a(n-2).

a(n) = n!*(2*n + 5 - (-1)^n)/4.

a(n) = n!*A004526(n+3). - R. J. Mathar, Nov 27 2011

Maple

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

Mathematica

With[{nn=20}, CoefficientList[Series[(1+x-x^2)/((1-x)(1-x^2)), {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Feb 10 2014 *)

Prog

(Magma) [Factorial(n)*(2*n+5-(-1)^n)/4: n in [0..30]]; // G. C. Greubel, Jun 02 2022
(SageMath) [factorial(n)*(n+2 + n%2)/2 for n in (0..40)] # G. C. Greubel, Jun 02 2022

Crossrefs

Cf. A000142, A004526.

Sequence in context: A226011 A174085 A325850 * A139104 A014448 A277033

Adjacent sequences: A052686 A052687 A052688 * A052690 A052691 A052692

Keyword

easy,nonn

Author

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

Status

approved