OFFSET
18,2
COMMENTS
Coordination sequence for 18-dimensional cyclotomic lattice Z[zeta_19].
Product of 18 consecutive numbers divided by 18!. - Artur Jasinski, Dec 02 2007
In this sequence only 19 is prime. - Artur Jasinski, Dec 02 2007
With a different offset, number of n-permutations (n>=18) of 2 objects: u,v, with repetition allowed, containing exactly (18) u's. - Zerinvary Lajos, Aug 04 2008
LINKS
T. D. Noe, Table of n, a(n) for n = 18..1000
Matthias Beck and Serkan Hosten, Cyclotomic polytopes and growth series of cyclotomic lattices, arXiv:math/0508136 [math.CO], 2005-2006.
Milan Janjic, Two Enumerative Functions.
Index entries for linear recurrences with constant coefficients, signature (19, -171, 969, -3876, 11628, -27132, 50388, -75582, 92378, -92378, 75582, -50388, 27132, -11628, 3876, -969, 171, -19, 1).
FORMULA
a(n+17) = n*(n+1)*(n+2)*(n+3)*(n+4)*(n+5)*(n+6)*(n+7)*(n+8)*(n+9)*(n+10)*(n+11)*(n+12)*(n+13)*(n+14)*(n+15)*(n+16)*(n+17)/18!. - Artur Jasinski, Dec 02 2007; R. J. Mathar, Jul 07 2009
G.f.: x^18/(1-x)^19. - Zerinvary Lajos, Aug 04 2008; R. J. Mathar, Jul 07 2009
From Amiram Eldar, Dec 10 2020: (Start)
Sum_{n>=18} 1/a(n) = 18/17.
MAPLE
seq(binomial(n, 18), n=18..38); # Zerinvary Lajos, Aug 04 2008
MATHEMATICA
Table[n(n+1)(n+2)(n+3)(n+4)(n+5)(n+6)(n+7)(n+8)(n+9)(n+10)(n+11)(n+12)(n+13)(n+14)(n+15)(n+16)(n+17)/18!, {n, 1, 100}] (* Artur Jasinski, Dec 02 2007 *)
Table[Binomial[n, 18], {n, 18, 50}] (* Vincenzo Librandi, Aug 08 2017 *)
PROG
(Magma) [Binomial(n, 18): n in [18..50]]; // Vincenzo Librandi, Aug 08 2017
(PARI) for(n=18, 50, print1(binomial(n, 18), ", ")) \\ G. C. Greubel, Nov 23 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
Some formulas adjusted to the offset by R. J. Mathar, Jul 07 2009
STATUS
approved