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%I #25 Sep 29 2023 13:09:28
%S 1,-2,20,-632,39440,-4087712,634237760,-137605112192,39776178356480,
%T -14775064298435072,6857795892626969600,-3889298341511511652352,
%U 2646362625886738240901120,-2127690488032789501903020032
%N Expansion of e.g.f. arcsinh(sin(x)) (odd powers only).
%C arcsinh(cos(x)*tan(x)) = x - 2/3!*x^3 + 20/5!*x^5 - 632/7!*x^7 + 39440/9!*x^9...
%C arcsin(sinh(x)) = x + 2*x^3/3! + 20*x^5/5! + 620*x^7/7! +...
%C arccosh(sin(x)) = Pi/2 - x + 2*x^3/3! - 20*x^5/5! + 620*x^7/7! -...
%H Nikolay Sh. Izmailian, Ralph Kenna, and Vladimir V. Papoyan, <a href="https://arxiv.org/abs/2303.03484">Exact coefficients of finite-size corrections in the Ising model with Brascamp-Kunz boundary conditions and their relationships for strip and cylindrical geometries</a>, arXiv:2303.03484 [cond-mat.stat-mech], 2023. See also <a href="https://doi.org/10.1088/1751-8121/acf96b">J. Phys. A: Math. Theor</a>, (2023).
%F a(n) ~ (-1)^n * 2^(2*n+5/4)*n^(2*n) / (exp(2*n)*log(1+sqrt(2))^(2*n+1/2)). - _Vaclav Kotesovec_, Oct 30 2013
%t Table[n!*SeriesCoefficient[ArcSinh[Sin[x]],{x,0,n}],{n,1,40,2}] (* _Vaclav Kotesovec_, Oct 30 2013 *)
%Y Cf. A101922.
%K sign
%O 0,2
%A Patrick Demichel (patrick.demichel(AT)hp.com)
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