A012825 Expansion of e.g.f. of arctan(sec(x)*arcsinh(x)) (odd coefficients only).

1, 0, 8, -392, 20096, -1754368, 241340032, -44833033216, 10840711614464, -3348758074142720, 1285112610745352192, -598690046386495291392, 332953969072425739124736, -217949438999618554495500288

Offset

0,3

Comments

arctan(sec(x)*arcsinh(x)) = x + 8/5!*x^5 - 392/7!*x^7 + 20096/9!*x^9 ...

Links

Table of n, a(n) for n=0..13.

Example

a(0) = 1! * (coefficient of x^1 term) = 1.
a(1) = 3! * (coefficient of x^3 term) = 0.
a(2) = 5! * (coefficient of x^5 term) = 8.

Mathematica

With[{nn=30}, Take[CoefficientList[Series[ArcTan[Sec[x]ArcSinh[x]], {x, 0, nn}], x] Range[0, nn-1]!, {2, -1, 2}]] (* Harvey P. Dale, Jul 31 2013 *)

Crossrefs

Sequence in context: A220799 A220785 A203368 * A221252 A165036 A185254

Adjacent sequences: A012822 A012823 A012824 * A012826 A012827 A012828

Keyword

sign

Author

Patrick Demichel (patrick.demichel(AT)hp.com)

Status

approved