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!)
 A003715 Expansion of e.g.f. sin(sin(sin(x))) (odd powers only). (Formerly M3134) 4
 1, -3, 33, -731, 25857, -1311379, 89060065, -7778778091, 849264442881, -113234181108643, 18073465545032353, -3395124358886313595, 740061366713642835201, -185005977382236600650035 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS {abs(a(n))} has e.g.f. sinh(sinh(sinh(x))) (odd powers only). - Jianing Song, Oct 25 2023 REFERENCES N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..100 FORMULA a(k) : =sum(j=0..k, (sum(m=j..k, (2^(-2*j-2*m)*(sum(i=0..(2*j+1)/2, (2*i-2*j-1)^(2*m+1)*(-1)^(i)*binomial(2*j+1,i)))*sum(i=0..(2*m+1)/2, (2*i-2*m-1)^(2*k+1)*binomial(2*m+1,i)*(-1)^(k-i)))/(2*m+1)!))/(2*j+1)!); [Vladimir Kruchinin, Jun 10 2011] MATHEMATICA With[{nn = 50}, Take[CoefficientList[Series[Sin[Sin[Sin[x]]], {x, 0, nn}], x] Range[0, nn - 1]!, {2, -1, 2}]] (* Vincenzo Librandi, Apr 11 2014 *) PROG (Maxima) a(k):=sum((sum((2^(-2*j-2*m)*(sum((2*i-2*j-1)^(2*m+1)*(-1)^(i)*binomial(2*j+1, i), i, 0, (2*j+1)/2))*sum((2*i-2*m-1)^(2*k+1)*binomial(2*m+1, i)*(-1)^(k-i), i, 0, (2*m+1)/2))/(2*m+1)!, m, j, k))/(2*j+1)!, j, 0, k). /* Vladimir Kruchinin, Jun 10 2011 */ CROSSREFS Cf. A003712. Sequence in context: A340971 A326328 A233319 * A247030 A009690 A229513 Adjacent sequences: A003712 A003713 A003714 * A003716 A003717 A003718 KEYWORD sign AUTHOR R. H. Hardin, Simon Plouffe 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 10 15:18 EST 2023. Contains 367713 sequences. (Running on oeis4.)