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A012495
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Expansion of e.g.f. arcsinh(sin(x)) (odd powers only).
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4
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1, -2, 20, -632, 39440, -4087712, 634237760, -137605112192, 39776178356480, -14775064298435072, 6857795892626969600, -3889298341511511652352, 2646362625886738240901120, -2127690488032789501903020032
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OFFSET
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0,2
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COMMENTS
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arcsinh(cos(x)*tan(x)) = x - 2/3!*x^3 + 20/5!*x^5 - 632/7!*x^7 + 39440/9!*x^9...
arcsin(sinh(x)) = x + 2*x^3/3! + 20*x^5/5! + 620*x^7/7! +...
arccosh(sin(x)) = Pi/2 - x + 2*x^3/3! - 20*x^5/5! + 620*x^7/7! -...
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LINKS
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FORMULA
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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
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MATHEMATICA
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Table[n!*SeriesCoefficient[ArcSinh[Sin[x]], {x, 0, n}], {n, 1, 40, 2}] (* Vaclav Kotesovec, Oct 30 2013 *)
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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Patrick Demichel (patrick.demichel(AT)hp.com)
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STATUS
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approved
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