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).
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..300
Roland Bacher and Philippe Flajolet, Pseudo-factorials, elliptic functions, and continued fractions, arXiv:0901.1379 [math.CA], 2009.
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.
G. Viennot, Une interprétation combinatoire des coefficients des développements en série entière des fonctions elliptiques de Jacobi, J. Combin. Theory, A 29 (1980), 121-133.
J. Tannery and J. Molk, Eléments de la Théorie des Fonctions Elliptiques (Vol. 4), Gauthier-Villars, Paris, 1902, p. 92.
Index entries for linear recurrences with constant coefficients, signature (11,-19,9).
FORMULA
From Michael Somos, Jun 27 2003: (Start)
G.f.: 4*x^2/((1-x)^2*(1-9*x)).
a(n) = (9^n-8*n-1)/16. (End)
a(n+2) = 4*A014832(n+1). [Bruno Berselli, Jun 29 2011]
MATHEMATICA
a[ n_] := If[ n < 0, 0, (-1)^n (2 n)! Coefficient[ SeriesCoefficient[ JacobiCN[x, m], {x, 0, 2 n}], m, 1]]; (* Michael Somos, Dec 27 2014 *)
LinearRecurrence[{11, -19, 9}, {0, 0, 4}, 21] (* Jean-François Alcover, Sep 21 2017 *)
PROG
(PARI) {a(n) = (9^n - 8*n -1) / 16}; /* Michael Somos, Jun 27 2003 */
(Magma) [(9^n-8*n-1)/16: n in [0..25]]; // Vincenzo Librandi, Jun 29 2011
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
More terms from Paolo Dominici (pl.dm(AT)libero.it) using formulas 16.22.1 and 16.22.2 of Abramowitz and Stegun's Handbook of Mathematical Functions.
STATUS
approved