A012115 Expansion of e.g.f. of cos(arcsin(arcsinh(x))), even powers only.

1, -1, 1, -49, 897, -96801, 6803457, -1275363153, 207592347393, -60889593787713, 17888210916886017, -7679611833095218545, 3530100224793651058305, -2109645360096014314212705, 1387893136694794953345211905, -1109191050707015380265790041745, 984063632341385922413073350925825

Offset: 0

Author

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

Keywords

• sign

Examples

			1 - 1/2!*x^2 + 1/4!*x^4 - 49/6!*x^6 + 897/8!*x^8...
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..224

Crossrefs

Cf. A012248.

Programs

Mathematica

With[{nn = 50}, Table[(CoefficientList[Series[Cos[ArcSin[ArcSinh[x]]], {x, 0, 2*nn}], x]*Range[0, 2*nn]!)[[n]], {n, 1, 2*nn + 1, 2}]] (* G. C. Greubel, Apr 12 2017 *)

PARI

x = 'x + O('x^40); select(x->x, Vec(serlaplace(cos(asin(asinh(x)))))) \\ Michel Marcus, Mar 09 2017

Extensions

More terms from Michel Marcus, Mar 09 2017