OFFSET
12,2
COMMENTS
Coordination sequence for 12-dimensional cyclotomic lattice Z[zeta_13].
In this sequence only 13 is prime. - Artur Jasinski, Dec 02 2007
LINKS
T. D. Noe, Table of n, a(n) for n = 12..1000
Matthias Beck and Serkan Hosten, Cyclotomic polytopes and growth series of cyclotomic lattices, arXiv:math/0508136 [math.CO], 2005-2006.
Index entries for linear recurrences with constant coefficients, signature (13, -78, 286, -715, 1287, -1716, 1716, -1287, 715, -286, 78, -13, 1).
FORMULA
a(n) = A110555(n+1,12). - Reinhard Zumkeller, Jul 27 2005
a(n+11) = n(n+1)(n+2)(n+3)(n+4)(n+5)(n+6)(n+7)(n+8)(n+9)(n+10)(n+11)/12!. - Artur Jasinski, Dec 02 2007, R. J. Mathar, Jul 07 2009
G.f.: x^12/(1-x)^13. - Zerinvary Lajos, Aug 06 2008, R. J. Mathar, Jul 07 2009
From Amiram Eldar, Dec 10 2020: (Start)
Sum_{n>=12} 1/a(n) = 12/11.
MAPLE
seq(binomial(n, 12), n=12..36); # Zerinvary Lajos, Aug 06 2008
MATHEMATICA
Table[Binomial[n, 12], {n, 12, 50}] (* Vladimir Joseph Stephan Orlovsky, Apr 22 2011 *)
PROG
(Magma) [Binomial(n, 12): n in [12..100]]; // Vincenzo Librandi, Apr 22 2011
(PARI) for(n=12, 50, print1(binomial(n, 12), ", ")) \\ G. C. Greubel, Aug 31 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
Some formulas referring to other offsets corrected by R. J. Mathar, Jul 07 2009
STATUS
approved