A301942 Expansion of e.g.f. arcsin(x)/cos(x) (odd powers only).

1, 4, 44, 1016, 42384, 2908544, 306305856, 46659144832, 9760451385600, 2683733034474496, 936308392553036800, 403127865773461755904, 209562975305232836300800, 129255511221696545852424192, 93252273300325219683758915584, 77766048645578119241905858314240

Offset: 0

Author

Ilya Gutkovskiy, Apr 09 2018

Keywords

• nonn

Examples

			arcsin(x)/cos(x) = x/1! + 4*x^3/3! + 44*x^5/5! + 1016*x^7/7! + 42384*x^9/9! + ...
		

Crossrefs

Cf. A000182, A000364, A000795, A001818, A002084, A003701, A003702, A012782, A296741, A302444, A302542, A302543.

Programs

Mathematica

nmax = 16; Table[(CoefficientList[Series[ArcSin[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)] arcsin(x)/cos(x).