The OEIS is supported by the many generous donors to the OEIS Foundation.

 Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”). Other ways to Give
 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A013524 Numerator of [x^(2n+1)] of the Taylor expansion tanh(cosec(x) - cot(x)). 1
 1, 0, -1, -1, -1, 13, 7951, 21599, -294997, -275833, -60527057, -6338125867, 37620769159, 10425684579701, 5113538085001361, -25594556368763237, -6013201989263028181, -3771502911169983097219, 18335649295377317231411, 669255665793644548301365603 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,6 COMMENTS The e.g.f. of x/2, tanh(cosec(x) - cot(x)) = x/(2^1*1!) - 8*x^5/(2^5*5!) - 112*x^7/(2^7*7!) - 128*x^9/(2^9*9!) + 109824*x^11/(2^11*11!) + ... is (up to signs) apparently provided by A003721. LINKS G. C. Greubel, Table of n, a(n) for n = 0..200 FORMULA a(n) = numerator([x^(2*n+1)] tanh(tan(x/2)). - Peter Luschny, Nov 14 2016 EXAMPLE Series starts: x/2 - x^5/480 - x^7/5760 - x^9/1451520 + 13*x^11/9676800 + 7951*x^13/49816166400 + ... MAPLE ser := series(tanh(tan(x/2)), x, 40): seq(numer(coeff(ser, x, 2*n+1)), n=0..19); # Peter Luschny, Nov 14 2016 MATHEMATICA Numerator[Take[CoefficientList[Series[Tanh[Csc[x] - Cot[x]], {x, 0, 40}], x], {2, -1, 2}]] (* G. C. Greubel, Nov 12 2016 *) CROSSREFS Sequence in context: A191937 A210157 A213410 * A060887 A020521 A208169 Adjacent sequences: A013521 A013522 A013523 * A013525 A013526 A013527 KEYWORD sign,frac AUTHOR Patrick Demichel (patrick.demichel(AT)hp.com) EXTENSIONS Name edited by R. J. Mathar, Dec 19 2011 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified November 29 03:18 EST 2022. Contains 358422 sequences. (Running on oeis4.)