OFFSET
1,1
COMMENTS
Terms with mod(n,4)=0 are zero, so a(n)=1 for those n.
arctan(1 + x) = Pi/4 + integral_{0..x} dt / (2 + 2*t + t^2). - Michael Somos, Apr 20 2014
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..1000
FORMULA
a(n) = Denominator(sum(k=1..n, (sum(i=1..k, (2^(i-n-1)*(-1)^(i+n+(k-1)/2)/i*binomial(k-1,k-i))))*binomial(n-1,n-k))). - Vladimir Kruchinin, Apr 17 2014
Empirical g.f.: -x*(16*x^11 -16*x^10 -16*x^9 -24*x^8 -8*x^7 +4*x^6 +12*x^5 +22*x^4 +x^3 +12*x^2 +4*x +2) / ((x -1)*(x +1)*(x^2 +1)*(2*x^2 -1)^2*(2*x^2 +1)^2). - Colin Barker, Apr 18 2014
MATHEMATICA
Table[Denominator[(-1)^n*2^(-n-1)*((1+I)^n-(1-I)^n)*I/n], {n, 1, 41}] (* Jean-François Alcover, Apr 18 2014, after Vladimir Kruchinin *)
PROG
(Maxima)
atan(n):=(sum((sum((2^(i-n-1)*(-1)^(i+n+(k-1)/2)/i*binomial(k-1, k-i)), i, 1, k))*binomial(n-1, n-k), k, 1, n));
makelist(denom(atan(n), n, 1, 10); /* Vladimir Kruchinin, Apr 17 2014 */
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Eric W. Weisstein, Sep 23 2002
STATUS
approved