A170920 Write x*cot(x) = Product_{n>=1} (1 + g_n*x^(2*n)); a(n) = numerator(g_n).

-1, -1, -1, -16, -91, -58844, -73267, -1196588, -49830764, -1715330699, -35249288479, -374085503198546, -732125336837021, -779432268293710651, -30015706187367326893, -183998031852529374082, -46789354983174555461, -115977125342651266593554, -248130101882943187003954597, -13171311382437535379302071714878

Offset: 1

Author

N. J. A. Sloane, Jan 31 2010

Keywords

• sign
• frac

Examples

			-1/3, -1/45, -1/105, -16/4725, -91/66825, -58844/127702575, -73267/383107725, ...
		

Crossrefs

Cf. A170921, A170908-A170919.

Programs

Maple

t1:=x*cot(x);
L:=100;
t0:=series(t1, x, L);
g:=[];
M:=20; # number of terms to get
t2:=t0:
for n from 1 to M do
t3:=coeff(t2, x, 2*n); t2:=series(t2/(1+t3*x^(2*n)), x, L); g:=[op(g), t3];
od:
g;
g1:=map(numer, g);
g2:=map(denom, g);

Extensions

Corrected definition and terms - N. J. A. Sloane, Oct 04 2019 (thanks to Petros Hadjicostas for pointing out that something was wrong).