A052739 E.g.f. (1-sqrt(1-4x-4x^2))/2 -x*(1+x).
0, 0, 2, 24, 288, 4800, 103680, 2741760, 85800960, 3100446720, 127037030400, 5819550105600, 294727768473600, 16350861400473600, 986127353590579200, 64238655955009536000, 4495021381191204864000, 336249161369543245824000
Offset: 0
Links
- INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 695
Programs
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Maple
spec := [S,{B=Prod(Z,Z),S=Prod(C,C),C=Union(B,S,Z)},labeled]: seq(combstruct[count](spec,size=n), n=0..20); -
Mathematica
With[{nn=20},CoefficientList[Series[(1-Sqrt[1-4x-4x^2])/2-x(1+x),{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, Jun 19 2018 *)
Formula
D-finite with recurrence: a(1)=0; a(2)=2; a(3)=24; a(4)=288; (-4*n^2+4)*a(n) +(-4*n-2)*a(n+1) +a(n+2)=0.
a(n) = A052727(n), n>2.- R. J. Mathar, Jan 26 2020