A353587 Denominators of coefficients c(n) in product expansion of (tan x)/x = Product_{k>=1} 1 + c(k)*x^(2k).

3, 15, 105, 2835, 66825, 3648645, 383107725, 97692469875, 1856156927625, 5568470782875, 9056719980433125, 33283445928091734375, 1298054391195577640625, 3952575621190533915703125, 367589532770719654160390625, 112527407991036628824609375, 3842566358093920359949921875

Offset

1,1

Comments

The coefficients of odd powers are zero since (tan x)/x is an even function.

Links

Table of n, a(n) for n=1..17.

Example

(tan x)/x = (1 + 1/3*x^2)(1 + 2/15*x^4)(1 + 1/105*x^6)(1 + 53/2835*x^8)...
and this sequence lists the denominators of (1/3, 2/15, 1/105, 53/2835, ...).

Prog

(PARI) t=tan(x+O(x)^58)/x; vector(#t\2, n, c=polcoef(t, n*2); t/=1+c*x^(n*2); denominator(c))

Crossrefs

Cf. A353586 (numerators); A353583 / A353584 (product expansion of 1 + tan x).

Cf. A170918 / A170919 for a variant.

Sequence in context: A269455 A088109 A231634 * A128276 A295124 A107878

Adjacent sequences: A353584 A353585 A353586 * A353588 A353589 A353590

Keyword

nonn,frac

Author

M. F. Hasler, May 07 2022

Status

approved