A052573 (1+3^n)*n!.

2, 4, 20, 168, 1968, 29280, 525600, 11027520, 264579840, 7142929920, 214280640000, 7071181286400, 254561568307200, 9927888709939200, 416971151460864000, 18763699200390144000, 900657519773147136000

Offset

0,1

Links

Table of n, a(n) for n=0..16.

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 516

Formula

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

D-finite Recurrence: {a(1)=4, a(0)=2, (3*n^2+9*n+6)*a(n)+(-4*n-8)*a(n+1)+a(n+2)=0}

(1+3^n)*n!

Maple

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

Mathematica

With[{nn=20}, CoefficientList[Series[-2(-1+2x)/(-1+x)/(-1+3x), {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Jul 04 2021 *)

Crossrefs

Sequence in context: A102087 A372234 A357671 * A110371 A120388 A061348

Adjacent sequences: A052570 A052571 A052572 * A052574 A052575 A052576

Keyword

easy,nonn

Author

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

Status

approved