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A301942 Expansion of e.g.f. arcsin(x)/cos(x) (odd powers only). 3
1, 4, 44, 1016, 42384, 2908544, 306305856, 46659144832, 9760451385600, 2683733034474496, 936308392553036800, 403127865773461755904, 209562975305232836300800, 129255511221696545852424192, 93252273300325219683758915584, 77766048645578119241905858314240 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..15.

FORMULA

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

EXAMPLE

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

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}]

CROSSREFS

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

Sequence in context: A206686 A302909 A053333 * A255928 A137783 A136552

Adjacent sequences:  A301939 A301940 A301941 * A301943 A301944 A301945

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Apr 09 2018

STATUS

approved

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Last modified July 7 16:01 EDT 2020. Contains 335496 sequences. (Running on oeis4.)