|
| |
|
|
A002754
|
|
Coefficients of elliptic function cn.
(Formerly M3680 N1501)
|
|
3
| |
|
|
0, 0, 4, 44, 408, 3688, 33212, 298932, 2690416, 24213776, 217924020, 1961316220, 17651846024, 158866614264, 1429799528428, 12868195755908, 115813761803232, 1042323856229152, 9380914706062436, 84428232354561996, 759854091191058040
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,3
|
|
|
REFERENCES
| A. Cayley, An Elementary Treatise on Elliptic Functions. Bell, London, 1895, p. 56.
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).
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.
|
|
|
LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..300
Roland Bacher and Philippe Flajolet, Pseudo-factorials, elliptic functions, and continued fractions.
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.
Index to sequences with linear recurrences with constant coefficients, signature (11,-19,9).
|
|
|
FORMULA
| G.f.: 4*x^2/((1-x)^2*(1-9*x)). a(n)=(9^n-8*n-1)/16. - Michael Somos, Jun 27, 2003
a(n+2) = 4*A014832(n+1). [Bruno Berselli, Jun 29 2011]
|
|
|
PROG
| (PARI) a(n)=(9^n-8*n-1)/16
(MAGMA)[(9^n-8*n-1)/16: n in [0..25]]; // Vincenzo Librandi, Jun 29 2011
|
|
|
CROSSREFS
| Cf. A060627, A014832.
Sequence in context: A178294 A043039 A198962 * A187870 A105038 A002278
Adjacent sequences: A002751 A002752 A002753 * A002755 A002756 A002757
|
|
|
KEYWORD
| nonn,easy
|
|
|
AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
|
|
|
EXTENSIONS
| 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.
|
| |
|
|
