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A013538 Numerator of [x^(2*n + 1)] in the Taylor series expansion of arcsin(cosec(x) - cotanh(x)). 2
-1, 53, 73, 45137, 11226497, 129163393, 474807665, 198247921612319, 618559606844489, 395129918156594369761, 2883495145728730085501149, 704455206007099333581073, 4366595916673463219275798447, 10742815369857597784418536545975463 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
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.
N. J. A. Sloane, List of Demichel sequences that need correcting, as of Dec 17 2011 [Thanks to D. S. McNeil for computing this list]
EXAMPLE
-1/6*x + 53/1296*x^3 + 73/145152*x^5 + 45137/156764160*x^7 + 11226497/893931945984*x^9 + ...
MAPLE
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);
MATHEMATICA
Numerator[Take[CoefficientList[Series[ArcSin[Csc[x] - Coth[x]], {x, 0, 26}], x], {2, -1, 2}]] (* G. C. Greubel, Nov 13 2016 *)
CROSSREFS
Cf. A202381.
Sequence in context: A133187 A057667 A160041 * A107309 A039389 A043212
KEYWORD
sign,frac
AUTHOR
Patrick Demichel (patrick.demichel(AT)hp.com)
EXTENSIONS
Corrected by N. J. A. Sloane, Dec 18 2011, based on discussions on the Sequence Fans Mailing List, Dec 13-17 2011
STATUS
approved

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Last modified March 28 18:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)