A012742 Expansion of e.g.f. arctan(arctanh(x)*cos(x)) (odd powers only).

1, -3, 53, -1799, 154985, -16589771, 3172731677, -721614303695, 241340829836497, -94965599172723859, 49224836859318783493, -29702702631352493918103, 22109389701103652762325561, -18928043482223039674124197467, 19177016900409865735958434301165, -22074310371520428549856056403952735

Offset

0,2

Links

Table of n, a(n) for n=0..15.

Example

E.g.f. = x - 3/3!*x^3 + 53/5!*x^5 - 1799/7!*x^7 + ...

Mathematica

With[{nn=30}, Take[CoefficientList[Series[ArcTan[ArcTanh[x]Cos[x]], {x, 0, nn}], x] Range[0, nn-1]!, {2, -1, 2}]] (* Harvey P. Dale, Nov 05 2015 *)

Crossrefs

Sequence in context: A273802 A216931 A352992 * A012823 A098932 A100444

Adjacent sequences: A012739 A012740 A012741 * A012743 A012744 A012745

Keyword

sign

Author

Patrick Demichel

Extensions

Definition modified by Harvey P. Dale, Nov 05 2015

a(13)-a(15) from Stefano Spezia, Oct 04 2025

Status

approved