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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

G. C. Greubel, Table of n, a(n) for n = 0..200

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

Adjacent sequences:  A013535 A013536 A013537 * A013539 A013540 A013541

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 August 20 11:39 EDT 2017. Contains 290835 sequences.