A052569 - OEIS

%I #20 Sep 25 2019 17:01:09

%S 1,1,2,12,48,240,2160,15120,120960,1451520,14515200,159667200,

%T 2395008000,31135104000,435891456000,7846046208000,125536739328000,

%U 2134124568576000,44816615940096000,851515702861824000

%N E.g.f. 1/((1-x)(1-x^3)).

%H Robert Israel, <a href="/A052569/b052569.txt">Table of n, a(n) for n = 0..448</a>

%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=512">Encyclopedia of Combinatorial Structures 512</a>

%F E.g.f.: 1/(-1+x)/(-1+x^3)

%F Recurrence: {a(1)=1, a(0)=1, a(2)=2, (-14*n-n^3-7*n^2-8)*a(n)+(-2-n)*a(n+1)+a(n+3)-a(n+2)=0}

%F (1/3*n+2/3+Sum(1/9*(-1+_alpha)*_alpha^(-1-n), _alpha=RootOf(_Z^2+_Z+1)))*n!

%F a(n) = n!*A008620(n). - _R. J. Mathar_, Nov 27 2011

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

%p # Alternative:

%p f:= gfun:-rectoproc({ a(1)=1, a(0)=1, a(2)=2, (-14*n-n^3-7*n^2-8)*a(n)+(-2-n)*a(n+1)+a(n+3)-a(n+2)=0},a(n),remember):

%p map(f, [$0..30]); # _Robert Israel_, Sep 25 2019

%t With[{nn=20},CoefficientList[Series[1/((1-x)(1-x^3)),{x,0,nn}],x]Range[0,nn]!] (* _Harvey P. Dale_, Aug 25 2012 *)

%K easy,nonn

%O 0,3

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