A302542 Expansion of e.g.f. arctan(x)/cos(x) (odd powers only).

1, 1, 29, -139, 31737, -1824151, 313750293, -51584719523, 13137192234225, -3947317975733039, 1522475446731094285, -702509124781480897211, 389722900767594460770025, -253710144786166583863030983, 192285396891961478711402819077, -167564604997707653568802119363795

Offset: 0

Author

Ilya Gutkovskiy, Apr 09 2018

Keywords

• sign

Examples

			arctan(x)/cos(x) = x/1! + x^3/3! + 29*x^5/5! - 139*x^7/7! + 31737*x^9/9! - 1824151*x^11/11! + ...
		

Crossrefs

Cf. A000182, A000364, A000795, A002084, A003701, A003702, A010050, A012801, A191003, A301942, A302444, A302543.

Programs

Mathematica

nmax = 16; Table[(CoefficientList[Series[ArcTan[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)] arctan(x)/cos(x).