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A002753 Coefficients of elliptic function sn.
(Formerly M4944 N2117)
4
1, 1, 14, 135, 5478, 165826, 13180268, 834687179, 109645021894, 11966116940238, 2347836365864484, 393938089395885894, 107947764316226205276, 25835579116799316507780 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

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, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

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 = 0..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.

C. L. Mallows, Letter to N. J. A. Sloane, May 16 1973

J. Tannery and J. Molk, Eléments de la Théorie des Fonctions Elliptiques (Vol. 4), Gauthier-Villars, Paris, 1902, p. 92.

FORMULA

a(n) ~ 2^(4*n + 13/2) * n^(2*n + 1) / (exp(2*n) * Pi^(2*n + 2)). - Vaclav Kotesovec, Apr 10 2018

MATHEMATICA

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 *)

CROSSREFS

Cf. A006089, A060628.

Sequence in context: A016801 A244651 A004004 * A155625 A016296 A021044

Adjacent sequences:  A002750 A002751 A002752 * A002754 A002755 A002756

KEYWORD

nonn

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

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Last modified November 12 12:43 EST 2018. Contains 317109 sequences. (Running on oeis4.)