A170921 Write x*cot(x) = Product_{n>=1} (1 + g_n*x^(2*n)); a(n) = denominator(g_n).

3, 45, 105, 4725, 66825, 127702575, 383107725, 18091198125, 1856156927625, 183759535834875, 9056719980433125, 275344870859667984375, 1298054391195577640625, 3952575621190533915703125, 367589532770719654160390625, 6249022057102234120726640625, 3842566358093920359949921875

Offset: 1

Author

N. J. A. Sloane, Jan 31 2010

Keywords

• nonn
• frac

Examples

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

Crossrefs

Cf. A170920.

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).