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!)
 A013518 Numerator of [x^(2n+1)] in the Taylor expansion arcsin(cosec(x)-cot(x)) = x/2 + x^3/16 + 3*x^5/256 + 83*x^7/30720 + 8887*x^9/12386304 + ... 1
 1, 1, 3, 83, 8887, 57539, 2419601, 298733192941, 84896691713, 54207578317691, 535009143553922969, 303988210353762448529, 39439620915967757710853, 18146112662693896499335287481 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS The e.g.f. of x/2, arcsin(cosec(x)-cot(x)) = x/(2^1*1!) + 3*x^3/(2^3*3!) + 45*x^5/(2^5*5!) +1743*x^7(/2^7*7!) + 133305*x^9/(2^9*9!) + ..., is apparently covered by A012780. LINKS G. C. Greubel, Table of n, a(n) for n = 0..216 FORMULA a(n)=(sum(k=0..n, (binomial(2*k,k)*sum(j=0..2*n-2*k, binomial(j+2*k,2*k)*(j+2*k+1)!*2^(-4*k-j-1)*(-1)^(n+k+j)*stirling2(2*n+1,j+2*k+1)))/(2*k+1)))/(2*n+1)!. - Vladimir Kruchinin, May 31 2013 MATHEMATICA Numerator[Take[CoefficientList[Series[ArcSin[Csc[x]-Cot[x]], {x, 0, 30}], x], {2, -1, 2}]] (* Harvey P. Dale, Feb 02 2012 *) PROG (Maxima) a(n):=(sum((binomial(2*k, k)*sum(binomial(j+2*k, 2*k)*(j+2*k+1)!*2^(-4*k-j-1)*(-1)^(n+k+j)*stirling2(2*n+1, j+2*k+1), j, 0, 2*n-2*k))/(2*k+1), k, 0, n))/(2*n+1)!; /* Vladimir Kruchinin, May 31 2013 */ CROSSREFS Cf. A089171. Sequence in context: A173811 A093166 A111648 * A166241 A140158 A160875 Adjacent sequences: A013515 A013516 A013517 * A013519 A013520 A013521 KEYWORD nonn,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 December 9 00:20 EST 2022. Contains 358698 sequences. (Running on oeis4.)