A052678 Expansion of e.g.f. x^3/(1-3*x).

0, 0, 0, 6, 72, 1080, 19440, 408240, 9797760, 264539520, 7936185600, 261894124800, 9428188492800, 367699351219200, 15443372751206400, 694951773804288000, 33357685142605824000, 1701241942272897024000

Offset

0,4

Links

G. C. Greubel, Table of n, a(n) for n = 0..350

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 626

Formula

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

Recurrence: a(0)=0, a(1)=0, a(2)=0, a(3)=6, a(n) = 3*n*a(n-1).

a(n) = 3^(n-3)*n!, n>2.

Maple

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

Mathematica

Table[If[n<3, 0, 3^(n-3)*n!], {n, 0, 30}] (* G. C. Greubel, Jun 11 2022 *)

Prog

(SageMath) [0, 0, 0]+[3^(n-3)*factorial(n) for n in (3..30)] # G. C. Greubel, Jun 11 2022

Crossrefs

Cf. A000142, A000244.

Sequence in context: A332705 A237021 A156128 * A052719 A196882 A289392

Adjacent sequences: A052675 A052676 A052677 * A052679 A052680 A052681

Keyword

easy,nonn

Author

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

Status

approved