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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
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
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.
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
Sequence in context: A323857 A244651 A004004 * A306301 A155625 A016296
KEYWORD
nonn
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