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%I #9 Oct 04 2019 22:19:03
%S -1,-1,-1,-16,-91,-58844,-73267,-1196588,-49830764,-1715330699,
%T -35249288479,-374085503198546,-732125336837021,-779432268293710651,
%U -30015706187367326893,-183998031852529374082,-46789354983174555461,-115977125342651266593554,-248130101882943187003954597,-13171311382437535379302071714878
%N Write x*cot(x) = Product_{n>=1} (1 + g_n*x^(2*n)); a(n) = numerator(g_n).
%e -1/3, -1/45, -1/105, -16/4725, -91/66825, -58844/127702575, -73267/383107725, ...
%p t1:=x*cot(x);
%p L:=100;
%p t0:=series(t1, x, L);
%p g:=[];
%p M:=20; # number of terms to get
%p t2:=t0:
%p for n from 1 to M do
%p t3:=coeff(t2, x, 2*n); t2:=series(t2/(1+t3*x^(2*n)), x, L); g:=[op(g), t3];
%p od:
%p g;
%p g1:=map(numer, g);
%p g2:=map(denom, g);
%Y Cf. A170921, A170908-A170919.
%K sign,frac
%O 1,4
%A _N. J. A. Sloane_, Jan 31 2010
%E Corrected definition and terms - _N. J. A. Sloane_, Oct 04 2019 (thanks to _Petros Hadjicostas_ for pointing out that something was wrong).