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A013334
Expansion of e.g.f. arcsinh(exp(x) - sec(x)).
1
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
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
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