A296623 Expansion of e.g.f. log(1 + arctan(x)*arctanh(x)) (even powers only).

0, 2, -12, 448, -21728, 2380032, -318185472, 69695846400, -18235768762368, 6697099792220160, -2892199532135841792, 1606188416621920911360, -1034069421398404544593920, 810882197441673837894696960, -727447103613537543910242385920, 766865924510666637669136261447680

Offset

0,2

Links

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

Formula

E.g.f.: log(1 + (i/4)*(log(1 - i*x) - log(1 + i*x))*(log(1 + x) - log(1 - x))), where i is the imaginary unit (even powers only).

Example

log(1 + arctan(x)*arctanh(x)) = 2*x^2/2! - 12*x^4/4! + 448*x^6/6! - 21728*x^8/8! + 2380032*x^10/10! - 318185472*x^12/12! + ...

Mathematica

nmax = 15; Table[(CoefficientList[Series[Log[1 + ArcTan[x] ArcTanh[x]], {x, 0, 2 nmax}], x] Range[0, 2 nmax]!)[[n]], {n, 1, 2 nmax + 1, 2}]
nmax = 15; Table[(CoefficientList[Series[Log[1 + (I/4) (Log[1 - I x] - Log[1 + I x]) (Log[1 + x] - Log[1 - x])], {x, 0, 2 nmax}], x] Range[0, 2 nmax]!)[[n]], {n, 1, 2 nmax + 1, 2}]

Crossrefs

Cf. A009272, A009398, A010050, A012727, A110708, A202139.

Sequence in context: A168504 A062738 A350790 * A009510 A091471 A357895

Adjacent sequences: A296620 A296621 A296622 * A296624 A296625 A296626

Keyword

sign

Author

Ilya Gutkovskiy, Dec 17 2017

Status

approved