A012588 Expansion of e.g.f. arctan(arcsinh(x) * exp(x)).

0, 1, 2, 0, -24, -132, 40, 8568, 83328, -44272, -13222112, -182425408, 173064320, 53699598912, 947897491840, -1462598830976, -450248068501504, -9631043314112256, 21880384337367552, 6765800654464927744, 169339160025954805760, -532061075701090923520, -165698959735673781516288

Offset

0,3

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..300

Example

x + 2/2!*x^2 - 24/4!*x^4 - 132/5!*x^5 + 40/6!*x^6 ...

Mathematica

Range[0, 19]! CoefficientList[Series[ArcTan[ArcSinh[x] Exp[x]], {x, 0, 19}], x] (* Vincenzo Librandi, Jul 20 2018 *)

Crossrefs

Sequence in context: A365980 A052607 A052602 * A012290 A012591 A319221

Adjacent sequences: A012585 A012586 A012587 * A012589 A012590 A012591

Keyword

sign

Author

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

Extensions

a(0) inserted and title improved by Sean A. Irvine, Jul 19 2018

Status

approved