A052601 E.g.f. (1-x)/(1-x-2x^3).

1, 0, 0, 12, 48, 240, 4320, 50400, 564480, 9434880, 166924800, 2953843200, 60354201600, 1357490534400, 31907254579200, 808142759424000, 22052620541952000, 635257746579456000, 19347973338710016000

Offset: 0

Author

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

Keywords

• easy
• nonn

Links

• INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 546

Programs

Maple

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

Formula

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

Recurrence: {a(1)=0, a(0)=1, a(2)=0, (-12*n^2-22*n-12-2*n^3)*a(n) +(-n-3)*a(n+2) +a(n+3)=0}

Sum(-1/29*(1+3*_alpha^2-10*_alpha)*_alpha^(-1-n), _alpha=RootOf(-1+_Z+2*_Z^3))*n!

a(n)= n!*A052537(n). - R. J. Mathar, Nov 27 2011