A006089 Coefficients of elliptic function cn.
16, 912, 30768, 870640, 22945056, 586629984, 14804306080, 371548371744, 9303419165040, 232733558500720, 5819812891661136, 145509858586733712, 3637888729721421568
Offset: 2
References
- M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, Tenth Printing, 1972, p. 575, Eq. 16.22.1 and 16.22.2.
- 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 = 2..100
- M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
- M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math.Series 55, Tenth Printing, 1972, p. 575, Eq. 16.22.1 and 16.22.2.
- A. Cayley, An Elementary Treatise on Elliptic Functions (page images), G. Bell and Sons, London, 1895, p. 56.
- J. Tannery and J. Molk, Eléments de la Théorie des Fonctions Elliptiques (Vol. 4), Gauthier-Villars, Paris, 1902, p. 92.
- G. Viennot, Une interprétation combinatoire des coefficients des développements en série entière des fonctions elliptiques de Jacobi, J. Combin. Theory, A 29 (1980), 121-133.
Crossrefs
Cf. A002753.
Programs
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Mathematica
max = 16; coes = Coefficient[#, m^2] & /@ CoefficientList[ Series[ JacobiCN[u, m], {u, 0, 2*max}, {m, 0, 2}], u]* Range[0, 2*max]!; a[n_] := Abs[ coes[[ 2*n+3 ]] ]; Table[ a[n], {n, 2, max-2}] (* Jean-François Alcover, Dec 20 2011 *)
Formula
a(n) ~ 25^(n+1) / 256. - Vaclav Kotesovec, Apr 10 2018
Extensions
More terms from Paolo Dominici (pl.dm(AT)libero.it) using formulas 16.22.1 and 16.22.2 of Abramowitz and Stegun's Handbook of Mathematical Functions