A047686 Denominators of coefficients in Taylor series for log(tan(x)/x).

1, 3, 90, 2835, 18900, 66825, 1915538625, 127702575, 186080895000, 350813659321125, 7656647326453125, 3018906660144375, 1211517431782539131250, 144228265688397515625, 564653660170076273671875, 84913182070036240111050234375, 499921764568178729658131250000

Offset

0,2

References

CRC Standard Mathematical Tables and Formulae, 30th ed. 1996, p. 42.

Jerome Spanier and Keith B. Oldham, "Atlas of Functions", Hemisphere Publishing Corp., 1987, chapter 34, equation 34:6:3 at page 323.

Links

Table of n, a(n) for n=0..16.

Index entries for Bernoulli numbers B(2n)

Formula

A047685(n)/a(n) = 2^(2n) *(2^(2n-1) -1) *abs(B(2n)) / ((2n)! *n).

Example

(1/3)*x^2 + (7/90)*x^4 + (62/2835)*x^6 + (127/18900)*x^8 + (146/66825)*x^10 + ...

Mathematica

Join[{1}, DeleteCases[Denominator[CoefficientList[Series[Log[Tan[x]/x], {x, 0, 33}], x]], 1]] (* Stefano Spezia, Jan 03 2025 *)

Crossrefs

Cf. A047685, B(2n)= A027641(2n) / A027642(2n).

Sequence in context: A254083 A103305 A097235 * A013304 A013298 A013302

Adjacent sequences: A047683 A047684 A047685 * A047687 A047688 A047689

Keyword

nonn,easy,frac

Author

N. J. A. Sloane

Status

approved