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%I M4944 N2117 #38 Oct 20 2023 09:42:47
%S 1,1,14,135,5478,165826,13180268,834687179,109645021894,
%T 11966116940238,2347836365864484,393938089395885894,
%U 107947764316226205276,25835579116799316507780
%N Coefficients of elliptic function sn.
%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, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Vincenzo Librandi, <a href="/A002753/b002753.txt">Table of n, a(n) for n = 0..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 C. L. Mallows, <a href="/A004004/a004004.pdf">Letter to N. J. A. Sloane, May 16 1973</a>.
%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.
%F a(n) ~ 2^(4*n + 13/2) * n^(2*n + 1) / (exp(2*n) * Pi^(2*n + 2)). - _Vaclav Kotesovec_, Apr 10 2018
%t lim = 14; se = Series[ JacobiSN[u, m], {u, 0, 2 lim -1}]; a[n_] := (-1)^n*Coefficient[ SeriesCoefficient[se, 2n + 1]*(2n + 1)!, m^Floor[n/2]]; a[0] = a[1] = 1; Table[a[n], {n, 0, lim-1}] (* _Jean-François Alcover_, Sep 21 2011 *)
%Y Cf. A006089, A060628.
%K nonn
%O 0,3
%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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