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%I M5026 #34 Oct 20 2023 10:01:16
%S 16,912,30768,870640,22945056,586629984,14804306080,371548371744,
%T 9303419165040,232733558500720,5819812891661136,145509858586733712,
%U 3637888729721421568
%N Coefficients of elliptic function cn.
%D 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.
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Vincenzo Librandi, <a href="/A006089/b006089.txt">Table of n, a(n) for n = 2..100</a>
%H M. Abramowitz and I. A. Stegun, eds., <a href="http://www.convertit.com/Go/ConvertIt/Reference/AMS55.ASP">Handbook of Mathematical Functions</a>, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
%H M. Abramowitz and I. A. Stegun, eds., <a href="http://www.convertit.com/Go/ConvertIt/Reference/AMS55.ASP">Handbook of Mathematical Functions</a>, National Bureau of Standards Applied Math.Series 55, Tenth Printing, 1972, p. 575, Eq. 16.22.1 and 16.22.2.
%H A. Cayley, <a href="http://cdl.library.cornell.edu/Hunter/hunter.pl?handle=cornell.library.math/Cayl005&id=7">An Elementary Treatise on Elliptic Functions</a> (page images), G. Bell and Sons, London, 1895, p. 56.
%H J. Tannery and J. Molk, <a href="http://gallica.bnf.fr/ark:/12148/bpt6k99586x/f104.image">Eléments de la Théorie des Fonctions Elliptiques (Vol. 4)</a>, Gauthier-Villars, Paris, 1902, p. 92.
%H G. Viennot, <a href="http://dx.doi.org/10.1016/0097-3165(80)90001-1">Une interprétation combinatoire des coefficients des développements en série entière des fonctions elliptiques de Jacobi</a>, J. Combin. Theory, A 29 (1980), 121-133.
%F a(n) ~ 25^(n+1) / 256. - _Vaclav Kotesovec_, Apr 10 2018
%t 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 *)
%Y Cf. A002753.
%K nonn,easy
%O 2,1
%A _N. J. A. Sloane_
%E 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
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