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
KEYWORD
nonn
AUTHOR
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