A052673 a(n) = 3*n*n!.

0, 3, 12, 54, 288, 1800, 12960, 105840, 967680, 9797760, 108864000, 1317254400, 17244057600, 242853811200, 3661488230400, 58845346560000, 1004293914624000, 18140058832896000, 345728180109312000

Offset: 0

Author

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

Keywords

• easy
• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..350
• INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 621
• Luis Manuel Rivera, Integer sequences and k-commuting permutations, arXiv preprint arXiv:1406.3081 [math.CO], 2014-2015.

Crossrefs

Cf. A083746, A122972.

Cf. A000142, A008585.

Programs

Magma

[3*(Factorial(n+1)-Factorial(n)): n in [0..30]]; // G. C. Greubel, Jun 12 2022

Maple

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

Mathematica

Table[3 n n!,{n,0,20}] (* Harvey P. Dale, Feb 12 2017 *)

SageMath

[3*n*factorial(n) for n in (0..30)] # G. C. Greubel, Jun 12 2022

Formula

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

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

a(n) = A122972(n+2) - A122972(n) for n > 0. - Reinhard Zumkeller, Sep 21 2006

For n>0: a(n) = A083746(n+2). - Reinhard Zumkeller, Apr 14 2007

G.f.: 3*Hypergeometric2F0([2,2], [], x). - G. C. Greubel, Jun 12 2022