A296742 Expansion of e.g.f. arcsinh(x*sec(x)) (odd powers only).

1, 2, 4, -8, 2448, 130976, -2342848, -239130240, 99052990720, 8918588764672, -2795242017684480, -92786315822417920, 279479081010906828800, -57316070780459900928, -39411396653183724314673152, 5932051008707372732672475136, 10689040617354387626585873252352

Offset

0,2

Links

Table of n, a(n) for n=0..16.

Formula

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

Example

arcsinh(x*sec(x)) = x/1! + 2*x^3/3! + 4*x^5/5! - 8*x^7/7! + 2448*x^9/9! + ...

Mathematica

nmax = 17; Table[(CoefficientList[Series[ArcSinh[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(asinh(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, A296741, A296743.

Sequence in context: A135212 A012456 A071686 * A103097 A335750 A062286

Adjacent sequences: A296739 A296740 A296741 * A296743 A296744 A296745

Keyword

sign

Author

Ilya Gutkovskiy, Dec 19 2017

Status

approved