A052621 E.g.f. (2+x+x^2+x^3)/(1-x^4).

2, 1, 2, 6, 48, 120, 720, 5040, 80640, 362880, 3628800, 39916800, 958003200, 6227020800, 87178291200, 1307674368000, 41845579776000, 355687428096000, 6402373705728000, 121645100408832000, 4865804016353280000

Offset

0,1

Links

Table of n, a(n) for n=0..20.

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 567

Formula

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

Recurrence: {a(1)=1, a(3)=6, a(2)=2, a(0)=2, (-n^4-35*n^2-50*n-24-10*n^3)*a(n)+a(n+4)=0}

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

2n! if n is 0 mod 4, n! otherwise.

a(n)=n!*A177704(n+3). - R. J. Mathar, Jun 03 2022

Maple

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

Mathematica

With[{nn=20}, CoefficientList[Series[(2+x+x^2+x^3)/(1-x^4), {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Oct 10 2023 *)

Crossrefs

Sequence in context: A000139 A302190 A114572 * A212671 A131057 A051852

Adjacent sequences: A052618 A052619 A052620 * A052622 A052623 A052624

Keyword

easy,nonn

Author

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

Status

approved