A052595 - OEIS

%I #16 Apr 18 2017 07:03:54

%S 1,3,20,198,2616,43200,856080,19792080,522950400,15544690560,

%T 513406252800,18652322304000,739253228313600,31740638183654400,

%U 1467650891266560000,72709824125562624000,3842307771930980352000

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

%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=540">Encyclopedia of Combinatorial Structures 540</a>

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

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

%F Sum(1/13*(2*_alpha+3)*_alpha^(-1-n), _alpha=RootOf(-1+3*_Z+_Z^2))*n!

%F a(n)= n!*A006190(n+1). - _R. J. Mathar_, Nov 27 2011

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

%K easy,nonn

%O 0,2

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