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%I #33 Dec 15 2023 15:45:05
%S 1,41,861,12341,135751,1221759,9366819,62891499,377348994,2054455634,
%T 10272278170,47626016970,206379406870,841392966470,3245372870670,
%U 11899700525790,41648951840265,139646485582065,449972009097765,1397281501935165,4191844505805495
%N Binomial coefficient C(n,40).
%C Coordination sequence for 40-dimensional cyclotomic lattice Z[zeta_41].
%H T. D. Noe, <a href="/A010993/b010993.txt">Table of n, a(n) for n = 40..1000</a>
%H Matthias Beck and Serkan Hosten, <a href="http://arxiv.org/abs/math/0508136">Cyclotomic polytopes and growth series of cyclotomic lattices</a>, arXiv:math/0508136 [math.CO], 2005-2006.
%H <a href="/index/Rec#order_41">Index entries for linear recurrences with constant coefficients</a>, 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).
%F G.f.: x^40/(1-x)^41. - _Zerinvary Lajos_, Dec 20 2008; adapted to offset by _Enxhell Luzhnica_, Jan 23 2017
%F From _Amiram Eldar_, Dec 15 2020: (Start)
%F Sum_{n>=40} 1/a(n) = 40/39.
%F Sum_{n>=40} (-1)^n/a(n) = A001787(40)*log(2) - A242091(40)/39! = 21990232555520*log(2) - 508996625841915892359554528/33393321606645 = 0.9766968066... (End)
%p seq(binomial(n,40),n=40..57); # _Zerinvary Lajos_, Dec 20 2008
%t Table[Binomial[n, 40], {n, 5!}] (* _Vladimir Joseph Stephan Orlovsky_, Sep 25 2008 *)
%o (Magma) [Binomial(n, 40): n in [40..70]]; // _Vincenzo Librandi_, Jun 12 2013
%Y Cf. A001787, A242091.
%K nonn
%O 40,2
%A _N. J. A. Sloane_
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