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Search: id:A002754
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| A002754 |
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Coefficients of elliptic function cn.
(Formerly M3680 N1501)
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+0
2
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| 0, 0, 4, 44, 408, 3688, 33212, 298932, 2690416, 24213776, 217924020, 1961316220, 17651846024, 158866614264, 1429799528428, 12868195755908, 115813761803232, 1042323856229152, 9380914706062436, 84428232354561996, 759854091191058040
(list; graph; listen)
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OFFSET
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0,3
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
R. BACHER AND P. FLAJOLET, PSEUDO-FACTORIALS, ELLIPTIC FUNCTIONS AND CONTINUED FRACTIONS, arXiv 0901.1379. [Added by N. J. A. Sloane (njas(AT)research.att.com), Feb 01 2009]
A. Cayley, An Elementary Treatise on Elliptic Functions. Bell, London, 1895, p. 56.
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
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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].
A. Cayley, An Elementary Treatise on Elliptic Functions (page images), G. Bell and Sons, London, 1895, p. 56.
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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FORMULA
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G.f.: 4x^2/((1-x)^2(1-9x)). a(n)=(9^n-8n-1)/16. - Michael Somos, Jun 27, 2003
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PROGRAM
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(PARI) a(n)=(9^n-8*n-1)/16
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CROSSREFS
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Cf. A060627.
Sequence in context: A035014 A030987 A043039 this_sequence A105038 A002278 A112897
Adjacent sequences: A002751 A002752 A002753 this_sequence A002755 A002756 A002757
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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More terms from Paolo Dominici (pl.dm(AT)libero.it) using formulae 16.22.1 and 16.22.2 of Abramowitz and Stegun's Handbook of Mathematical Functions.
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