A006089 Coefficients of elliptic function cn. (Formerly M5026)

16, 912, 30768, 870640, 22945056, 586629984, 14804306080, 371548371744, 9303419165040, 232733558500720, 5819812891661136, 145509858586733712, 3637888729721421568

Offset

2,1

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.

Formula

a(n) ~ 25^(n+1) / 256. - Vaclav Kotesovec, Apr 10 2018

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 *)

Crossrefs

Cf. A002753.

Sequence in context: A369583 A283946 A289707 * A260620 A290940 A173953

Adjacent sequences: A006086 A006087 A006088 * A006090 A006091 A006092

Keyword

nonn,easy

Author

N. J. A. Sloane

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

Status

approved