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

0,4

Links

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

Example

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

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 *)

Prog

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

Crossrefs

Cf. A012248.

Sequence in context: A278284 A110906 A193940 * A284642 A304046 A264877

Adjacent sequences: A012112 A012113 A012114 * A012116 A012117 A012118

Keyword

sign

Author

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

Extensions

More terms from Michel Marcus, Mar 09 2017

Status

approved