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A180657 Numerator of the fraction tan( sum_{k=1..n} arctan(k)). 1
1, -3, 0, 4, -9, 105, -308, 36, -423, 2387, -26004, 104472, -50617, 119889, -5466072, 3154072, 51692571, -2921193, 351666136, -1278405156, 11188330461, -68445012691, 553299094188, -4915961459556 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..24.

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 *)

CROSSREFS

For denominators see A220447.

Sequence in context: A079406 A068627 A074171 * A094665 A052439 A261239

Adjacent sequences:  A180654 A180655 A180656 * A180658 A180659 A180660

KEYWORD

sign,frac,easy

AUTHOR

R. J. Mathar, Jan 21 2011

STATUS

approved

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Last modified February 19 11:04 EST 2018. Contains 299330 sequences. (Running on oeis4.)