A302543 Expansion of e.g.f. arctanh(x)/cos(x) (odd powers only).

1, 5, 69, 2001, 104073, 8723549, 1088372557, 190057979177, 44285819490065, 13267464006201781, 4964113699657822805, 2266816666007859759489, 1239999748307938170531225, 800189083150907165762837517, 601369618369661775955962338653, 520607107122686183781743903500505

Offset: 0

Author

Ilya Gutkovskiy, Apr 09 2018

Keywords

• nonn

Examples

			arctanh(x)/cos(x) = x/1! + 5*x^3/3! + 69*x^5/5! + 2001*x^7/7! + 104073*x^9/9! + ...
		

Crossrefs

Cf. A000182, A000364, A000795, A002084, A003701, A003702, A010050, A012840, A296743, A301942, A302444, A302542.

Programs

Mathematica

nmax = 16; Table[(CoefficientList[Series[ArcTanh[x]/Cos[x], {x, 0, 2 nmax + 1}], x] Range[0, 2 nmax + 1]!)[[n]], {n, 2, 2 nmax, 2}]

Formula

a(n) = (2*n+1)! * [x^(2*n+1)] arctanh(x)/cos(x).