A052631 a(n) = n!*Pell(n) (or n!*A000129(n)).

0, 1, 4, 30, 288, 3480, 50400, 851760, 16450560, 357436800, 8629286400, 229162348800, 6638962176000, 208362342988800, 7042436719718400, 255029193619200000, 9851119008546816000, 404305986955014144000, 17569457946995834880000, 805912049524456562688000

Offset: 0

Author

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

Keywords

• easy
• nonn

Links

• INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 577

Programs

Maple

spec := [S,{S=Prod(Z,Sequence(Union(Z,Z,Prod(Z,Z))))},labeled]: seq(combstruct[count](spec,size=n), n=0..20);
with(combstruct):ZL:=[T,{T=Union(Z,Prod(Epsilon,Z,T),Prod(T,Z,Epsilon),Prod(T,Z,Z))},labeled]:seq(count(ZL,size=i),i=0..19); # Zerinvary Lajos, Dec 16 2007

Formula

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

Recurrence: {a(1)=1, a(0)=0, (-2-n^2-3*n)*a(n)+(-4-2*n)*a(n+1)+a(n+2)}.

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