A052588 Expansion of e..g.f.: (1-x)/(1-x-x^2-x^3+x^4).
1, 0, 2, 12, 48, 600, 5760, 65520, 967680, 14515200, 250387200, 4790016000, 98195328000, 2204365363200, 53178757632000, 1371750412032000, 37828404117504000, 1107254963662848000, 34316723062702080000
Offset: 0
Links
- INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 533
Programs
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Maple
spec := [S,{S=Sequence(Prod(Z,Z,Union(Z,Sequence(Z))))},labeled]: seq(combstruct[count](spec,size=n), n=0..20); -
Mathematica
With[{nn=20},CoefficientList[Series[(1-x)/(1-x-x^2-x^3+x^4),{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, Jul 22 2024 *)
Formula
E.g.f.: -(-1+x)/(1-x-x^3+x^4-x^2)
Recurrence: {a(1)=0, a(0)=1, a(2)=2, a(3)=12, (n^4+35*n^2+50*n+24+10*n^3)*a(n) +(-n^3-9*n^2-26*n-24)*a(n+1) +(-n^2-7*n-12)*a(n+2) +(-n-4)*a(n+3) +a(n+4)=0}
Sum(-1/39*(-2-11*_alpha+4*_alpha^2+_alpha^3)*_alpha^(-1-n), _alpha=RootOf(1-_Z-_Z^3+_Z^4-_Z^2))*n!
a(n) = n!*A052527(n). - R. J. Mathar
Extensions
Definition clarified by Harvey P. Dale, Jul 22 2024