A052761 a(n) = 3!*n*S(n-1,3), where S denotes the Stirling numbers of second kind.

0, 0, 0, 0, 24, 180, 900, 3780, 14448, 52164, 181500, 615780, 2052072, 6749028, 21976500, 71007300, 228009696, 728451972, 2317445100, 7346047140, 23213772120, 73156412196, 229989358500, 721474964100, 2258832312144, 7059480120900, 22026886599900

Offset

0,5

Links

Matthew House, Table of n, a(n) for n = 0..2079

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 718

Index entries for linear recurrences with constant coefficients, signature (12,-58,144,-193,132,-36).

Formula

E.g.f.: exp(x)^3*x - 3*exp(x)^2*x + 3*x*exp(x) - x.

Recurrence: {a(1)=0, a(2)=0, a(3)=0, a(4)=24, (-36*n^2 - 66*n - 6*n^3 - 36)*a(n) + (11*n^3 + 55*n^2 + 66*n)*a(n+1) + (-6*n^3 - 24*n^2 - 18*n)*a(n+2) + (n^3 + 3*n^2 + 2*n)*a(n+3)}

For n>=2, a(n) = n*(3^(n-1) - 3*2^(n-1) + 3). - Vaclav Kotesovec, Nov 27 2012

O.g.f.: 12*x^4*(2 - 9*x + 11*x^2 - 3*x^3)/((1 - 3*x)^2*(1 - 2*x)^2*(1 - x)^2). - Matthew House, Feb 16 2017 [Corrected by Georg Fischer, May 19 2019]

From Andrew Howroyd, Aug 08 2020: (Start)

a(n) = n*A001117(n-1) for n > 1.

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

Maple

spec := [S, {B=Set(Z, 1 <= card), S=Prod(B, B, B, Z)}, labeled]: seq(combstruct[count](spec, size=n), n=0..20);

Mathematica

Join[{0}, Table[3!*n*StirlingS2[n-1, 3], {n, 30}]] (* Harvey P. Dale, Feb 07 2015 *)

Prog

(PARI) a(n)={if(n>=1, 3!*n*stirling(n-1, 3, 2), 0)} \\ Andrew Howroyd, Aug 08 2020

Crossrefs

Cf. A000392, A001117, A052749.

Sequence in context: A372521 A297522 A165187 * A392821 A392851 A371158

Adjacent sequences: A052758 A052759 A052760 * A052762 A052763 A052764

Keyword

nonn,easy

Author

INRIA Encyclopedia of Combinatorial Structures, Jan 25 2000

Extensions

Better description from Victor Adamchik (adamchik(AT)cs.cmu.edu), Jul 19 2001

More terms from Harvey P. Dale, Feb 07 2015

Status

approved