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

0,4

Links

Table of n, a(n) for n=0..27.

Formula

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

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 *)

Crossrefs

Sequence in context: A025262 A056010 A002712 * A193418 A005960 A273716

Adjacent sequences: A192676 A192677 A192678 * A192680 A192681 A192682

Keyword

nonn

Author

Emanuele Munarini, Jul 07 2011

Status

approved