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 A003715 E.g.f. sin(sin(sin(x))) (odd powers only). (Formerly M3134) 3
 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 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 Sequence in context: A144756 A326328 A233319 * A247030 A009690 A229513 Adjacent sequences:  A003712 A003713 A003714 * A003716 A003717 A003718 KEYWORD sign AUTHOR STATUS approved

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Last modified February 17 02:22 EST 2020. Contains 331976 sequences. (Running on oeis4.)