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%I A285019 #13 Apr 10 2017 12:40:34
%S A285019 1,1,1,5,35,7,77,143,715,12155,46189,29393,676039,1300075,185725,
%T A285019 1077205,33393355,21607465,756261275,1472719325,3829070245,
%U A285019 22427411435,87670790155,19058867425,895766768975,1755702867191
%N A285019 Numerator of (-1/3)^n*sqrt(Pi)/(Gamma(1/2 - n)*Gamma(1 + n)).
%F A285019 a(n)/A285018(n) = (-1/3)^n*sqrt(Pi)/(Gamma(1/2 - n)*Gamma(1 + n)).
%F A285019 Sum_{k>=0} a(k)/A285018(k) = sqrt(3/2).
%F A285019 Sum_{k>=0} (-1)^k*a(k)/A285018(k) = sqrt(3)/2.
%F A285019 Sum_{k>=0} (-1)^(k+1)*a(k)/A285018(k) = -sqrt(3)/2.
%p A285019 P:=proc(q) numer((-1/3)^q*sqrt(Pi)/(GAMMA(1/2-q)*GAMMA(1+q))); end:
%p A285019 seq(P(i),i=0..25); # _Paolo P. Lava_, Apr 10 2017
%t A285019 Numerator[Table[(-1/3)^n*Sqrt[Pi]/(Gamma[1/2-n]*Gamma[1+n]),{n,0,25}]]
%Y A285019 Cf. A285018 (denominators).
%K A285019 nonn,frac
%O A285019 0,4
%A A285019 _Ralf Steiner_, Apr 08 2017

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