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%I #23 Apr 09 2018 22:32:49
%S 1,4,44,1016,42384,2908544,306305856,46659144832,9760451385600,
%T 2683733034474496,936308392553036800,403127865773461755904,
%U 209562975305232836300800,129255511221696545852424192,93252273300325219683758915584,77766048645578119241905858314240
%N Expansion of e.g.f. arcsin(x)/cos(x) (odd powers only).
%F a(n) = (2*n+1)! * [x^(2*n+1)] arcsin(x)/cos(x).
%e arcsin(x)/cos(x) = x/1! + 4*x^3/3! + 44*x^5/5! + 1016*x^7/7! + 42384*x^9/9! + ...
%t 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}]
%Y Cf. A000182, A000364, A000795, A001818, A002084, A003701, A003702, A012782, A296741, A302444, A302542, A302543.
%K nonn
%O 0,2
%A _Ilya Gutkovskiy_, Apr 09 2018