A052620 - OEIS

%I #13 Jun 03 2022 18:51:32

%S 1,1,8,66,768,11040,190800,3845520,88583040,2295578880,66098592000,

%T 2093556326400,72337863628800,2707751497651200,109153235884492800,

%U 4714413247095552000,217193790828478464000,10631538129843671040000

%N E.g.f. (1-x)^2/(1-3x+x^3).

%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=566">Encyclopedia of Combinatorial Structures 566</a>

%F E.g.f.: (-1+x)^2/(1-3*x+x^3)

%F Recurrence: {a(1)=1, a(0)=1, a(2)=8, (n^3+6*n^2+11*n+6)*a(n) +(-3*n-9)*a(n+2) +a(n+3)=0}

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

%F a(n) = n!*A052545(n). - _R. J. Mathar_, Jun 03 2022

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

%K easy,nonn

%O 0,3

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