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A004004
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(3^{2n+1} - 8n - 3)/16.
(Formerly M4943)
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8
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0, 1, 14, 135, 1228, 11069, 99642, 896803, 8071256, 72641337, 653772070, 5883948671, 52955538084, 476599842805, 4289398585298, 38604587267739, 347441285409712, 3126971568687473
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Contribution from Johannes W. Meijer (meijgia(AT)hotmail.com), Jun 27 2009: The o.g.f. of this sequence enabled the analysis of A162008, A162009 and A162010.
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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.
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
| 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.
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FORMULA
| Contribution from Johannes W. Meijer (meijgia(AT)hotmail.com), Jun 27 2009: (Start)
a(n) = 11*a(n-1)-19*a(n-2)+9*a(n-3)
(End)
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MAPLE
| A004004:=-z*(1+3*z)/(9*z-1)/(z-1)**2; [Conjectured by S. Plouffe in his 1992 dissertation.]
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CROSSREFS
| Contribution from Johannes W. Meijer (meijgia(AT)hotmail.com), Jun 27 2009: (Start)
Equals the second right hand column of triangle A162005 divided by 2.
Cf. A162008, A162009, A162010, A162011 and A162014 [2*(1+3*z)].
(End)
Sequence in context: A164598 A073554 A016801 * A002753 A155625 A016296
Adjacent sequences: A004001 A004002 A004003 * A004005 A004006 A004007
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KEYWORD
| nonn
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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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