Search: id:A004005
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%I A004005 M5397
%S A004005 1,135,5478,165826,4494351,116294673,2949965020,74197080276,
%T A004005 1859539731885,46535238000235,1163848723925346,29100851707716150,
%U A004005 727566807977891803,18189614152200873621,454744658216502193656
%N A004005 Coefficients of elliptic function sn.
%D A004005 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A004005 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.
%D A004005 A. Fransen, Conjectures on the Taylor series expansion coefficients of 
               the Jacobian elliptic function sn(n,k), Math. Comp., 37 (1981), 475-497.
%D A004005 I. P. Goulden and D. M. Jackson, Combinatorial Enumeration, Wiley, N.Y., 
               1983,(5.2.24).
%D A004005 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.
%H A004005 S. Plouffe, <a href="http://www.lacim.uqam.ca/%7Eplouffe/articles/MasterThesis.pdf">
               Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures</
               a>, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 
               1992.
%H A004005 S. Plouffe, <a href="http://www.lacim.uqam.ca/%7Eplouffe/articles/FonctionsGeneratrices.pdf">
               1031 Generating Functions and Conjectures</a>, Universit\'{e} du 
               Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
%H A004005 A. Cayley, <a href="http://cdl.library.cornell.edu/Hunter/hunter.pl?handle=cornell.library.math/
               Cayl005&id=7">An Elementary Treatise on Elliptic Functions</a> (page 
               images), G. Bell and Sons, London, 1895, p. 56.
%H A004005 J. Tannery and J. Molk, <a href="http://gallica.bnf.fr/scripts/ConsultationTout.exe?E=0&O=N099586">
               El\'{e}ments de la Th\'{e}orie des Fonctions Elliptiques (Vol. 4)</
               a>, Gauthier-Villars, Paris, 1902, p. 92.
%p A004005 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.]
%Y A004005 Leading terms in rows of triangle in A060628.
%Y A004005 Sequence in context: A159201 A157734 A061073 this_sequence A143404 A051028 
               A076011
%Y A004005 Adjacent sequences: A004002 A004003 A004004 this_sequence A004006 A004007 
               A004008
%K A004005 nonn,nice,easy
%O A004005 2,2
%A A004005 N. J. A. Sloane (njas(AT)research.att.com), Simon Plouffe (simon.plouffe(AT)gmail.com)
%E A004005 More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Mar 
               29 2003

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