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Floor-Sqrt transform of ordered Bell numbers (A000670).
0

%I #7 Mar 30 2016 23:00:21

%S 1,1,1,3,8,23,68,217,738,2662,10111,40281,167605,725850,3262107,

%T 15175084,72908536,361068922,1839982245,9633358049,51746379547,

%U 284824200163,1604632175859,9243292234736,54390064543757,326645626694244,2000556362576213,12485902607285611

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

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

%t FSFromExpSeries[f_,x_,n_] := Map[Floor[Sqrt[#]]&,CoefficientList[Series[f,{x,0,n}],x]Table[k!,{k,0,n}]]

%t FSFromExpSeries[1/(2-Exp[x]),x,40]

%t (* second program: *)

%t 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 *)

%K nonn

%O 0,4

%A _Emanuele Munarini_, Jul 07 2011