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A004005
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Coefficients of elliptic function sn.
(Formerly M5397)
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3
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1, 135, 5478, 165826, 4494351, 116294673, 2949965020, 74197080276, 1859539731885, 46535238000235, 1163848723925346, 29100851707716150, 727566807977891803, 18189614152200873621, 454744658216502193656
(list; graph; refs; listen; history; internal format)
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OFFSET
| 2,2
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REFERENCES
| A. Fransen, Conjectures on the Taylor series expansion coefficients of the Jacobian elliptic function sn(n,k), Math. Comp., 37 (1981), 475-497.
I. P. Goulden and D. M. Jackson, Combinatorial Enumeration, Wiley, N.Y., 1983,(5.2.24).
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
| A. Cayley, An Elementary Treatise on Elliptic Functions (page images), G. Bell and Sons, London, 1895, p. 56.
S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
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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MAPLE
| A004005:=-(-1-89*z+69*z**2+405*z**3)/(-1+25*z)/(9*z-1)**2/(z-1)**3; [Conjectured by S. Plouffe in his 1992 dissertation.]
A004005 := proc(n) A060628(n, 2) ; end proc: seq(A004005(n), n=2..40) ; # R. J. Mathar, Jan 30 2011
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CROSSREFS
| Leading terms in rows of triangle in A060628.
Sequence in context: A157734 A061073 A195671 * A143404 A051028 A076011
Adjacent sequences: A004002 A004003 A004004 * A004006 A004007 A004008
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KEYWORD
| nonn,nice,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Simon Plouffe (simon.plouffe(AT)gmail.com)
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EXTENSIONS
| More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Mar 29 2003
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