A302444 Expansion of e.g.f. arcsinh(x)/cos(x) (odd powers only).

1, 2, 24, 216, 15936, -77056, 90991744, -8523712768, 2731708067840, -684815907467264, 268028469798256640, -114888252320482000896, 62022733722259702579200, -38635369828053720937463808, 28349537098304682205749968896, -23874826868622028919177351004160

Offset: 0

Author

Ilya Gutkovskiy, Apr 09 2018

Keywords

• sign

Examples

			arcsinh(x)/cos(x) = x/1! + 2*x^3/3! + 24*x^5/5! + 216*x^7/7! + 15936*x^9/9! - 77056*x^11/11! + ...
		

Crossrefs

Cf. A000182, A000364, A000795, A001818, A002084, A003701, A003702, A012821, A296742, A301942, A302542, A302543.

Programs

Mathematica

nmax = 16; Table[(CoefficientList[Series[ArcSinh[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)] arcsinh(x)/cos(x).