A013334 Expansion of e.g.f. arcsinh(exp(x) - sec(x)).

0, 1, 0, 0, -4, 0, 0, 0, -1104, -5040, 0, 184800, -1784704, -39948480, -201801600, 2969366400, 24788541696, -621491320320, -12903078988800, 20131497484800, 2944178363780096, 8434762785469440, -1051002016730265600, -14118259471683840000, 255660771276061802496

Offset

0,5

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Example

x - 4/4!*x^4 - 1104/8!*x^8 - 5040/9!*x^9 ...

Mathematica

Range[0, 30]! CoefficientList[Series[ArcSinh[Exp[x] - Sec[x]], {x, 0, 30}], x] (* Vincenzo Librandi, Aug 06 2018 *)

Prog

(Magma)  m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!(1+Argsinh(Exp(x) - Sec(x)))); [0] cat [Factorial(n-1)*b[n]: n in [2..m]]; // Vincenzo Librandi, Aug 06 2018
(PARI) x = 'x + O('x^30); concat(0, Vec(serlaplace(asinh(exp(x) - 1/cos(x))))) \\ Michel Marcus, Aug 06 2018

Crossrefs

Sequence in context: A101193 A258646 A258647 * A258648 A185232 A258649

Adjacent sequences: A013331 A013332 A013333 * A013335 A013336 A013337

Keyword

sign

Author

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

Extensions

a(0)=0 inserted and title improved by Sean A. Irvine, Aug 05 2018

Status

approved