A052610 E.g.f. 1/(1-x-2x^3).

1, 1, 2, 18, 120, 840, 9360, 115920, 1491840, 22861440, 395539200, 7304774400, 148011494400, 3281639961600, 77850214041600, 1975895970048000, 53666956062720000, 1547595999645696000, 47204701332332544000

Offset: 0

Author

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

Keywords

• easy
• nonn

Links

• INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 555

Programs

Maple

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

Formula

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

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

Sum(1/29*(2+6*_alpha^2+9*_alpha)*_alpha^(-1-n), _alpha=RootOf(-1+_Z+2*_Z^3))*n!

a(n)=n!*A077949(n). - R. J. Mathar, Jun 03 2022