A012857 Numerator of [x^(2n)] of the Taylor expansion log(cosec(x)*arctan(x)).

0, -1, 3, -50, 203, -7472, 319561, -4725019, 8552625673, -2454640799284, 16155306808034, -5947223237624953, 147005475101499533, -2545370372470913809, 7441717839455761431719, -508348729177729085598593, 406949946622639944716921263, -22131398651123280388913461556

Offset

0,3

Comments

The inner function is cosec(x)*arctan(x) = 1 - x^2/6 + 59*x^4/360 - 1723*x^6/15120 + 164597*x^8/1814400 - ...

Links

Table of n, a(n) for n=0..17.

Example

-x^2/6 + 3*x^4/20 - 50*x^6/567 + 203*x^8/3240 - 7472*x^10/155925 + ...

Crossrefs

Cf. A175671 (denominators).

Sequence in context: A356640 A350810 A356642 * A246221 A249249 A034201

Adjacent sequences: A012854 A012855 A012856 * A012858 A012859 A012860

Keyword

sign,frac

Author

Patrick Demichel

Extensions

Values replaced by numerators by R. J. Mathar, Dec 20 2011

More terms from Jason Yuen, Sep 27 2025

Status

approved