A052791 3^(n-3)*n*(n-1)*(n-2).

0, 0, 0, 6, 72, 540, 3240, 17010, 81648, 367416, 1574640, 6495390, 25981560, 101328084, 386889048, 1450833930, 5356925280, 19514513520, 70252248672, 250273635894, 883318714920, 3091615502220, 10739295955080, 37050571045026, 127030529297232, 433058622604200, 1468633589701200

Offset: 0

Author

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

Keywords

• easy
• nonn

Comments

The number of surjective functions f:{1,2,...,n}->{1,2,3} with a designated pre-image of 1, 2, and 3.

Links

• INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 748
• Index entries for linear recurrences with constant coefficients, signature (12,-54,108,-81).

Crossrefs

Cf. A001815.

Programs

Maple

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

Mathematica

Range[0, 20]! CoefficientList[Series[(x Exp[x])^3, {x, 0, 20}], x]
LinearRecurrence[{12,-54,108,-81},{0,0,0,6},30] (* Harvey P. Dale, Sep 02 2022 *)

PARI

a(n)=3^(n-3)*n*(n-1)*(n-2); /* Joerg Arndt, Sep 16 2012 */

Formula

E.g.f.: x^3*exp(x)^3

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

a(n) = n!*sum(i+j+k=n, ijk/(i!j!k!)) - Benoit Cloitre, Nov 11 2004

G.f.: 6*x^3 / (3*x-1)^4. - Colin Barker, Jun 04 2013

Extensions

Edited by N. J. A. Sloane, Dec 24 2010