OFFSET
40,2
COMMENTS
Coordination sequence for 40-dimensional cyclotomic lattice Z[zeta_41].
LINKS
T. D. Noe, Table of n, a(n) for n = 40..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 (41, -820, 10660, -101270, 749398, -4496388, 22481940, -95548245, 350343565, -1121099408, 3159461968, -7898654920, 17620076360, -35240152720, 63432274896, -103077446706, 151584480450, -202112640600, 244662670200, -269128937220, 269128937220, -244662670200, 202112640600, -151584480450, 103077446706, -63432274896, 35240152720, -17620076360, 7898654920, -3159461968, 1121099408, -350343565, 95548245, -22481940, 4496388, -749398, 101270, -10660, 820, -41, 1).
FORMULA
G.f.: x^40/(1-x)^41. - Zerinvary Lajos, Dec 20 2008; adapted to offset by Enxhell Luzhnica, Jan 23 2017
From Amiram Eldar, Dec 15 2020: (Start)
Sum_{n>=40} 1/a(n) = 40/39.
MAPLE
seq(binomial(n, 40), n=40..57); # Zerinvary Lajos, Dec 20 2008
MATHEMATICA
Table[Binomial[n, 40], {n, 5!}] (* Vladimir Joseph Stephan Orlovsky, Sep 25 2008 *)
PROG
(Magma) [Binomial(n, 40): n in [40..70]]; // Vincenzo Librandi, Jun 12 2013
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved