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A013538 Numerator of [x^(2*n + 1)] in the Taylor series expansion of arcsin(cosec(x) - cotanh(x)). 2


%S -1,53,73,45137,11226497,129163393,474807665,198247921612319,

%T 618559606844489,395129918156594369761,2883495145728730085501149,

%U 704455206007099333581073,4366595916673463219275798447,10742815369857597784418536545975463

%N Numerator of [x^(2*n + 1)] in the Taylor series expansion of arcsin(cosec(x) - cotanh(x)).

%H G. C. Greubel, <a href="/A013538/b013538.txt">Table of n, a(n) for n = 0..200</a>

%H N. J. A. Sloane, <a href="/A013538/a013538.txt">The file Demichel1.txt</a>. 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.

%H N. J. A. Sloane, <a href="/A013538/a013538_1.txt">List of Demichel sequences that need correcting, as of Dec 17 2011</a> [Thanks to D. S. McNeil for computing this list]

%e -1/6*x + 53/1296*x^3 + 73/145152*x^5 + 45137/156764160*x^7 + 11226497/893931945984*x^9 + ...

%p t1:=arcsin(csc(x)-coth(x));

%p t2:=series(t1,x,30);

%p t3:=seriestolist(t2);

%p t3:=[seq(t3[2*i],i=1..(nops(t3)-2)/2 )];

%p t4:=map(numer,t3); t5:=map(denom,t3); lprint(t2);

%t Numerator[Take[CoefficientList[Series[ArcSin[Csc[x] - Coth[x]], {x,0,26}], x], {2, -1, 2}]] (* _G. C. Greubel_, Nov 13 2016 *)

%Y Cf. A202381.

%K sign,frac

%O 0,2

%A Patrick Demichel (patrick.demichel(AT)hp.com)

%E 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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Last modified September 21 08:38 EDT 2020. Contains 337268 sequences. (Running on oeis4.)