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
KEYWORD
nonn,easy
AUTHOR
encyclopedia(AT)pommard.inria.fr, 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