A052567 E.g.f.: (1-x)^2/(1-3*x+x^2).

1, 1, 6, 48, 504, 6600, 103680, 1900080, 39795840, 937681920, 24548832000, 706966444800, 22210346188800, 755916735974400, 27706219904563200, 1088037381150720000, 45576301518139392000, 2028445209752113152000, 95589693062063456256000, 4754884242802394308608000

Offset: 0

Author

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

Keywords

• easy
• nonn

Links

• INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 509

Crossrefs

Cf. A000142, A001906, A005443, A088305.

Programs

Maple

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

Mathematica

With[{nn=20},CoefficientList[Series[(1-x)^2/(1-3x+x^2),{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, Jul 06 2021 *)

Formula

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

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

Sum(-1/5*(3*_alpha-2)*_alpha^(-1-n), _alpha=RootOf(_Z^2-3*_Z+1))*n!

a(n) = n! * Fibonacci(2*n) for n > 0. - Ilya Gutkovskiy, Jul 17 2021