A003715 Expansion of e.g.f. sin(sin(sin(x))) (odd powers only). (Formerly M3134)

1, -3, 33, -731, 25857, -1311379, 89060065, -7778778091, 849264442881, -113234181108643, 18073465545032353, -3395124358886313595, 740061366713642835201, -185005977382236600650035

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