A296741 Expansion of e.g.f. arcsin(x*sec(x)) (odd powers only).

1, 4, 64, 2752, 237312, 34390016, 7512117248, 2302977392640, 942529341030400, 496287845973753856, 326775812392982937600, 263039306566659448242176, 254121613033387345942937600, 290175686081926976733941071872, 386599796043915196967089006968832

Offset

0,2

Links

Table of n, a(n) for n=0..14.

Formula

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

Example

arcsin(x*sec(x)) = x/1! + 4*x^3/3! + 64*x^5/5! + 2752*x^7/7! + 237312*x^9/9! + ...

Mathematica

nmax = 15; Table[(CoefficientList[Series[ArcSin[x Sec[x]], {x, 0, 2 nmax + 1}], x] Range[0, 2 nmax + 1]!)[[n]], {n, 2, 2 nmax, 2}]

Prog

(PARI) first(n) = x='x+O('x^(2*n)); vecextract(Vec(serlaplace(asin(x/cos(x)))), (4^n - 1)/3) \\ Iain Fox, Dec 19 2017

Crossrefs

Cf. A001818, A003700, A009118, A009119, A009562, A009563, A009765, A009843, A102072, A191003, A296464, A296466, A296679, A296680, A296742, A296743.

Sequence in context: A261042 A002454 A013043 * A167406 A156631 A088065

Adjacent sequences: A296738 A296739 A296740 * A296742 A296743 A296744

Keyword

nonn

Author

Ilya Gutkovskiy, Dec 19 2017

Status

approved