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%I #32 Dec 17 2015 09:43:22
%S 2,1,3,-1,12,1,30,1,35,-1,56,1,90,1,99,-1,132,1,182,1,195,-1,240,1,
%T 306,1,323,-1,380,1,462,1,483,-1,552,1,650,1,675,-1,756,1,870,1,899,
%U -1,992,1,1122,1,1155,-1,1260
%N First denominator and then numerator in a fraction expansion of log(2) - Pi/8.
%C The minus sign in front of a fraction is considered the sign of the numerator.
%D Mohammad K. Azarian, Problem 1218, Pi Mu Epsilon Journal, Vol. 13, No. 2, Spring 2010, p. 116. Solution published in Vol. 13, No. 3, Fall 2010, pp. 183-185.
%D Granino A. Korn and Theresa M. Korn, Mathematical Handbook for Scientists and Engineers, McGraw-Hill Book Company, New York (1968).
%F log(2) - Pi/8 = Sum_{n>=1} (-1)^(n+1)*(1/n) + (-1/2)*Sum_{n>=0} (-1)^n*(1/(2*n+1)).
%F Empirical g.f.: x*(2+x+x^2-2*x^3+9*x^4+2*x^5+14*x^6-2*x^7+3*x^8+2*x^9+3*x^10-2*x^11+x^13) / ((1-x)^3*(1+x)^3*(1-x+x^2)^2*(1+x+x^2)^2). - _Colin Barker_, Dec 17 2015
%e 1/2 - 1/3 + 1/12 + 1/30 - 1/35 + 1/56 + 1/90 - 1/99 + 1/132 + 1/182 - 1/195 + 1/240 + ... = [(1 - 1/2) + (1/3 - 1/4) + (1/5 - 1/6) + (1/7 - 1/8) + (1/9 - 1/10) + (1/11 - 1/12) + ... ] - (1/2)*[(1 - 1/3) + (1/5 - 1/7) + (1/9 - 1/11) + (1/13 - 1/15) + ... ] = log(2) - Pi/8.
%Y Cf. A164833, A195908, A195909, A195913, A016655, A019675, A075549, A098289, A118324, A144981, A161685, A168056, A004772.
%K frac,sign
%O 1,1
%A _Mohammad K. Azarian_, Sep 25 2011
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