OFFSET
1,2
LINKS
T. Amdeberhan, Luis A. Medina and V. H. Moll, Arithmetical properties of a sequence arising from an arctangent sum, J. Number Theory 128 (2008) 1807-1846.
V. H. Moll, An arithmetic conjecture on a sequence of arctangent sums, 2012. - From N. J. A. Sloane, Dec 22 2012
FORMULA
Let x(1)=1 and x(n) = (x(n-1)+n)/(1-n*x(n-1)). Then a(n) = numerator(x(n)).
EXAMPLE
The fractions are x(1)=1, x(2)=-3, x(3)=0, x(4)=4, x(5)=-9/19, x(6)=105/73 etc.
MAPLE
A := proc(n) local x, itr; x := 1 ; for itr from 2 to n do x := (x+itr)/(1-itr*x) ; end do; numer(x) ; end proc:
seq(A(n), n=1..30) ;
MATHEMATICA
x[1] := 1; x[n_] := (x[n - 1] + n)/(1 - n * x[n - 1]); Table[Numerator[x[n]], {n, 10}] (* Alonso del Arte, Jan 21 2011 *)
(* Just for verification: *)
x[n_] := Tan[Sum[ArcTan[k], {k, n}]] // TrigExpand;
Table[x[n] // Numerator, {n, 24}] (* Jean-François Alcover, Mar 29 2020 *)
CROSSREFS
KEYWORD
sign,frac,easy
AUTHOR
R. J. Mathar, Jan 21 2011
STATUS
approved