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A006089
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Coefficients of elliptic function cn.
(Formerly M5026)
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1
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16, 912, 30768, 870640, 22945056, 586629984, 14804306080, 371548371744, 9303419165040, 232733558500720, 5819812891661136, 145509858586733712, 3637888729721421568
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OFFSET
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2,1
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REFERENCES
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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).
G. Viennot, Une interpretation combinatoire des coefficients des developpements en serie entiere des fonctions elliptiques de Jacobi, J. Combin. Theory, A 29 (1980), 121-133.
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LINKS
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Table of n, a(n) for n=2..14.
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, El\'{e}ments de la Th\'{e}orie des Fonctions Elliptiques (Vol. 4), Gauthier-Villars, Paris, 1902, p. 92.
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MATHEMATICA
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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}] (* From Jean-François Alcover, Dec 20 2011 *)
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CROSSREFS
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Sequence in context: A145243 A214386 A185561 * A173953 A211105 A211081
Adjacent sequences: A006086 A006087 A006088 * A006090 A006091 A006092
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane.
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EXTENSIONS
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More terms from Paolo Dominici (pl.dm(AT)libero.it) using formulae 16.22.1 and 16.22.2 of Abramowitz and Stegun's Handbook of Mathematical Functions.
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STATUS
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approved
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