A052726 E.g.f. (1-sqrt(1-4*x-4*x^2))/ (2*(1+x)).

0, 1, 2, 18, 216, 3720, 81360, 2172240, 68423040, 2484639360, 102190636800, 4695453100800, 238382331264000, 13251891094041600, 800600878273996800, 52229642780899584000, 3659347096696811520000, 274040260725697449984000

Offset: 0

Author

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

Keywords

• easy
• nonn

Links

• INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 682

Programs

Maple

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

Mathematica

With[{nn=20},CoefficientList[Series[(1-Sqrt[1-4x-4x^2])/(2(1+x)),{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, Feb 15 2020 *)

Formula

D-finite with recurrence: {a(1)=1, a(0)=0, a(2)=2, (-4*n^3-12*n^2-8*n)*a(n) +(-22*n-12-8*n^2)*a(n+1) +(-3*n-3)*a(n+2) +a(n+3) =0.

a(n) = n!*A052709(n). - R. J. Mathar, Oct 18 2013