OFFSET
0,3
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..350
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 636
FORMULA
Recurrence: a(0)=0, a(1)=1, a(2)=2, (n+2)*a(n+3) = (n+3)*a(n+2) + (n+2)*(n+3)*a(n+1) + (n+1)*(n+2)*(n+3)^2*a(n).
a(n) = (n!/3)*(n + 1 - (1/3)*Sum_{alpha=RootOf(Z^2 + Z + 1)} (1 + 2*alpha)*_alpha^(-1-n)).
a(n) = n!*A002264(n+2). - R. J. Mathar, Nov 27 2011
MAPLE
spec := [S, {S=Prod(Z, Sequence(Z), Sequence(Prod(Z, Z, Z)))}, labeled]: seq(combstruct[count](spec, size=n), n=0..20);
G(x):=x/(1-x)/(1-x^3): f[0]:=G(x): for n from 1 to 19 do f[n]:=diff(f[n-1], x) od: x:=0: seq(f[n], n=0..19); # Zerinvary Lajos, Apr 03 2009
MATHEMATICA
With[{nn=20}, CoefficientList[Series[x/((1-x)(1-x^3)), {x, 0, nn}], x] Range[ 0, nn]!] (* Harvey P. Dale, Dec 24 2018 *)
Table[n!*Floor[(n+2)/3], {n, 0, 40}] (* G. C. Greubel, Jun 02 2022 *)
PROG
(SageMath) [factorial(n)*((n+2)//3) for n in (0..40)] # G. C. Greubel, Jun 02 2022
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
encyclopedia(AT)pommard.inria.fr, Jan 25 2000
STATUS
approved