A353586 Numerators of coefficients c(n) in product expansion of (tan x)/x = Product_{k>=1} 1 + c(k)*x^(2k).

1, 2, 1, 53, 91, 811, 73267, 35540711, 49830764, 34241488, 35249288479, 19259769465311, 732125336837021, 619038578481164306, 30015706187367326893, 16177789439326291541, 46789354983174555461, 498213391899375541476686, 248130101882943187003954597, 2572596069535443792125179632949

Offset

1,2

Comments

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

See A353587 for the denominators, and A353583 (similar for 1 + tan x) for references and more.

Links

Table of n, a(n) for n=1..20.

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 numerators 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); numerator(c))

Crossrefs

Cf. A353587 (denominators); A353583 / A353584 (product expansion of 1 + tan x).

Cf. A170918 / A170919 for a variant.

Sequence in context: A225778 A271442 A092650 * A363381 A221194 A309207

Adjacent sequences: A353583 A353584 A353585 * A353587 A353588 A353589

Keyword

nonn,frac

Author

M. F. Hasler, May 07 2022

Status

approved