|
%I M3134 #28 Oct 25 2023 09:28:12
%S 1,-3,33,-731,25857,-1311379,89060065,-7778778091,849264442881,
%T -113234181108643,18073465545032353,-3395124358886313595,
%U 740061366713642835201,-185005977382236600650035
%N Expansion of e.g.f. sin(sin(sin(x))) (odd powers only).
%C {abs(a(n))} has e.g.f. sinh(sinh(sinh(x))) (odd powers only). - _Jianing Song_, Oct 25 2023
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Vincenzo Librandi, <a href="/A003715/b003715.txt">Table of n, a(n) for n = 0..100</a>
%F 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]
%t 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 *)
%o (Maxima)
%o 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 */
%Y Cf. A003712.
%K sign
%O 0,2
%A _R. H. Hardin_, _Simon Plouffe_
|
