A101922 Numerators of expansion of e.g.f. 2^(-1/2) * arcsinh(cos(x)), even powers only.
-1, -1, 11, 491, 11159, -460681, -103577629, -8160790429, 624333860399, 386787409545839, 68810049201689531, -6999828208693648549, -9872674440874152431161, -3255253386897615662908441, 346248578699462435167833491, 1072454627614122049417452882131
Offset: 1
Keywords
Programs
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Mathematica
Table[Numerator[(2n)!SeriesCoefficient[ArcSinh[Cos[x]]/Sqrt[2],{x,0,2n}]],{n,14}] (* Stefano Spezia, Aug 29 2022 *) -
PARI
lista(nn) = my(x='x + O('x^(nn+1)), p=serlaplace(asinh(cos(x))/sqrt(2))); vector(nn\2, k, round(polcoef(p, 2*k)*2^k)); \\ Michel Marcus, Sep 11 2022
Formula
arcsinh(cos(x)) = log(sqrt(2)+1) + 1/sqrt(2) * (-(1/2)*x^2/2! - (1/4)*x^4/4! + (11/8)*x^6/6! + (491/16)*x^8/8! + ...).
arccosh(cos(x)) = Pi/2 - log(sqrt(2)+1) + 1/sqrt(2) * ((1/2)*x^2/2! + (1/4)*x^4/4! - (11/8)*x^6/6! - (491/16)*x^8/8! - ...).
a(n) = - A263246(n). - Michel Marcus, Sep 11 2022
Extensions
More terms from Michel Marcus, Sep 11 2022
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