OFFSET
0,3
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..375
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 648
FORMULA
E.g.f.: x/((1-x)*(1-3*x)).
D-finite Recurrence: a(0) = 0, a(1)=1, a(n) = 4*n*a(n-1) - 3*n*(n-1)*a(n-2).
a(n) = (3^n - 1)*n!/2.
a(n) = n!*A003462(n). - R. J. Mathar, Nov 27 2011
MAPLE
spec := [S, {S=Prod(Z, Sequence(Z), Sequence(Union(Z, Z, Z)))}, labeled]: seq(combstruct[count](spec, size=n), n=0..20);
MATHEMATICA
With[{nn=20}, CoefficientList[Series[x/((1-x)(1-3x)), {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Nov 05 2014 *)
Table[(3^n-1)*n!/2, {n, 0, 30}] (* G. C. Greubel, May 31 2022 *)
PROG
(SageMath) [(3^n-1)*factorial(n)/2 for n in (0..30)] # G. C. Greubel, May 31 2022
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
encyclopedia(AT)pommard.inria.fr, Jan 25 2000
STATUS
approved