A052666 E.g.f. 1/(1-x-3x^2).
1, 1, 8, 42, 456, 4800, 69840, 1093680, 20482560, 420577920, 9736070400, 245887488000, 6806133734400, 203555082931200, 6565920180019200, 226728504946944000, 8355118608764928000, 327047476385710080000
Offset: 0
Links
- INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 613
Programs
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Maple
spec := [S,{S=Sequence(Union(Z,Prod(Z,Union(Z,Z,Z))))},labeled]: seq(combstruct[count](spec,size=n), n=0..20);
Formula
E.g.f.: -1/(-1+x+3*x^2)
Recurrence: {a(1)=1, a(0)=1, (-3*n^2-9*n-6)*a(n)+(-2-n)*a(n+1)+a(n+2)=0}
Sum(1/13*(1+6*_alpha)*_alpha^(-1-n), _alpha=RootOf(-1+_Z+3*_Z^2))*n!
a(n) = n!*A006130(n). - R. J. Mathar, Nov 27 2011