A192679 Floor-Sqrt transform of ordered Bell numbers (A000670).

1, 1, 1, 3, 8, 23, 68, 217, 738, 2662, 10111, 40281, 167605, 725850, 3262107, 15175084, 72908536, 361068922, 1839982245, 9633358049, 51746379547, 284824200163, 1604632175859, 9243292234736, 54390064543757, 326645626694244, 2000556362576213, 12485902607285611

Offset: 0

Author

Emanuele Munarini, Jul 07 2011

Keywords

• nonn

Programs

Mathematica

FSFromExpSeries[f_,x_,n_] := Map[Floor[Sqrt[#]]&,CoefficientList[Series[f,{x,0,n}],x]Table[k!,{k,0,n}]]
FSFromExpSeries[1/(2-Exp[x]),x,40]
(* second program: *)
Fubini[n_, r_] := Sum[k!*Sum[(-1)^(i+k+r)*(i+r)^(n-r)/(i!*(k-i-r)!), {i, 0, k-r}], {k, r, n}]; Fubini[0, 1] = 1; a[n_] := Fubini[n, 1] // Sqrt // Floor; Table[a[n], {n, 0, 27}] (* Jean-François Alcover, Mar 30 2016 *)

Formula

a(n) = floor(sqrt(orderedBell(n))).