A052590 - OEIS

%I #17 Apr 18 2017 07:03:54

%S 1,3,20,204,2784,47520,973440,23264640,635443200,19525847040,

%T 666654105600,25037094297600,1025783842406400,45529186384281600,

%U 2176249118883840000,111452688851632128000,6088372509440212992000

%N E.g.f. (1-x)/(1-4x+2x^2).

%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=535">Encyclopedia of Combinatorial Structures 535</a>

%F E.g.f.: -(-1+x)/(1-4*x+2*x^2)

%F Recurrence: {a(0)=1, a(1)=3, (2*n^2+6*n+4)*a(n)+(-4*n-8)*a(n+1)+a(n+2)=0}

%F Sum(1/4*_alpha^(-1-n), _alpha=RootOf(1-4*_Z+2*_Z^2))*n!

%F a(n) =n!*A007052(n). - _R. J. Mathar_, Nov 27 2011

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

%t With[{nn=20},CoefficientList[Series[(1-x)/(1-4x+2x^2),{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, Jan 10 2014 *)

%K easy,nonn

%O 0,2

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