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A013538
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Numerator of [x^(2*n + 1)] in the Taylor series expansion of arcsin(cosec(x) - cotanh(x)).
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2
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-1, 53, 73, 45137, 11226497, 129163393, 474807665, 198247921612319, 618559606844489, 395129918156594369761, 2883495145728730085501149, 704455206007099333581073, 4366595916673463219275798447, 10742815369857597784418536545975463
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OFFSET
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0,2
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LINKS
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N. J. A. Sloane, The file Demichel1.txt. This shows all the sequences in this family as they were originally sent to me in May 1996. Most are correct, but several have small errors and about 64 of them are simply wrong. They are in the process of being corrected.
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EXAMPLE
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-1/6*x + 53/1296*x^3 + 73/145152*x^5 + 45137/156764160*x^7 + 11226497/893931945984*x^9 + ...
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MAPLE
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t1:=arcsin(csc(x)-coth(x));
t2:=series(t1, x, 30);
t3:=seriestolist(t2);
t3:=[seq(t3[2*i], i=1..(nops(t3)-2)/2 )];
t4:=map(numer, t3); t5:=map(denom, t3); lprint(t2);
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MATHEMATICA
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Numerator[Take[CoefficientList[Series[ArcSin[Csc[x] - Coth[x]], {x, 0, 26}], x], {2, -1, 2}]] (* G. C. Greubel, Nov 13 2016 *)
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CROSSREFS
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KEYWORD
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sign,frac
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AUTHOR
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Patrick Demichel (patrick.demichel(AT)hp.com)
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EXTENSIONS
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Corrected by N. J. A. Sloane, Dec 18 2011, based on discussions on the Sequence Fans Mailing List, Dec 13-17 2011
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STATUS
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approved
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