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A101928
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Expansion of cos(asinh(x)) = sin(acosh(x)).
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1
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1, -1, 5, -85, 3145, -204425, 20646925, -2993804125, 589779412625, -151573309044625, 49261325439503125, -19753791501240753125, 9580588878101765265625, -5527999782664718558265625
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| Absolute values are expansion of cosh(asin(x)).
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FORMULA
| E.g.f.: cos(arcsinh(x)) = sqrt(1+x^2)*(1-x^2*(1-5*x^2/(G(0)+5*x^2))) ; G(k) = (k+2)*(2*k+3)-x^2*(2*k^2+6*k+5)+x^2*(k+2)*(2*k+3)*(2*k^2+10*k+13)/G(k+1) ;
for cosh(arcsin(x)) = sqrt(1-x^2)*(1 + x^2*(1 + 5*x^2/(G(0) - 5*x^2))); G(k) = x^2*(2*k^2+6*k+5) + (k+2)*(2*k+3) - x^2*(k+2)*(2*k+3)*(2*k^2+10*k+13)/G(k+1) ; (continued fraction). - Sergei N. Gladkovskii, Dec 19 2011
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EXAMPLE
| cos(asinh(x)) = 1 - x^2/2 + 5x^4/4! - 85x^6/6! + 3145x^8/8! -...
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CROSSREFS
| Bisection of A006228.
Sequence in context: A195156 A188918 A203800 * A012788 A192055 A012815
Adjacent sequences: A101925 A101926 A101927 * A101929 A101930 A101931
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KEYWORD
| sign
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AUTHOR
| Ralf Stephan, Dec 28 2004
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