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 60th year, we have over 367,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”). Other ways to Give
 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A012022 Expansion of e.g.f.: arctan(sin(arctan(x))) (odd powers only). 1
 1, -5, 129, -7965, 903105, -163451925, 43259364225, -15764670046125, 7571150452490625, -4634731528895593125, 3522824632122301130625, -3255279003622294051528125, 3593928024032353882700450625 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..100 FORMULA a(n) = (2*n+1)!*(-1)^n*Sum_{j=1..n+1} binomial((2*n-1)/2, n+1-j) /(2*j-1). - Vladimir Kruchinin, May 19 2011 E.g.f.: Sum_{n >= 0} a(n)*x^(2n+1)/(2n+1)! = arctan(sin(arctan(x))). a(n) = (2*n+1)! * [x^(2*n+1)] arctan(sin(arctan(x))). MATHEMATICA With[{nn=30}, Take[CoefficientList[Series[ArcTan[Sin[ArcTan[x]]], {x, 0, nn}], x] Range[0, nn-1]!, {2, -1, 2}]] (* Harvey P. Dale, Dec 11 2013 *) PROG (Maxima) a(n):= ((2*n+1)!* (-1)^n *sum(binomial((2*n-1)/2, n+1-j)/(2*j-1), j, 1, n+1)); /* Vladimir Kruchinin, May 19 2011 */ CROSSREFS Sequence in context: A094074 A012218 A012136 * A012176 A012187 A012083 Adjacent sequences: A012019 A012020 A012021 * A012023 A012024 A012025 KEYWORD sign AUTHOR Patrick Demichel (patrick.demichel(AT)hp.com) 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 December 7 22:54 EST 2023. Contains 367662 sequences. (Running on oeis4.)