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A010989 Binomial coefficient C(n,36).

%I A010989 #33 Dec 15 2023 10:58:20
%S A010989 1,37,703,9139,91390,749398,5245786,32224114,177232627,886163135,
%T A010989 4076350421,17417133617,69668534468,262596783764,937845656300,
%U A010989 3188675231420,10363194502115,32308782859535,96926348578605,280576272201225,785613562163430,2132379668729310
%N A010989 Binomial coefficient C(n,36).
%C A010989 Coordination sequence for 36-dimensional cyclotomic lattice Z[zeta_37].
%H A010989 T. D. Noe, <a href="/A010989/b010989.txt">Table of n, a(n) for n = 36..1000</a>
%H A010989 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 A010989 <a href="/index/Rec#order_37">Index entries for linear recurrences with constant coefficients</a>, signature (37, -666, 7770, -66045, 435897, -2324784, 10295472, -38608020, 124403620, -348330136, 854992152, -1852482996, 3562467300, -6107086800, 9364199760, -12875774670, 15905368710, -17672631900, 17672631900, -15905368710, 12875774670, -9364199760, 6107086800, -3562467300, 1852482996, -854992152, 348330136, -124403620, 38608020, -10295472, 2324784, -435897, 66045, -7770, 666, -37, 1).
%F A010989 G.f.: x^36/(1-x)^37. - _Zerinvary Lajos_, Dec 19 2008; adapted to offset by _Enxhell Luzhnica_, Jan 23 2017
%F A010989 From _Amiram Eldar_, Dec 12 2020: (Start)
%F A010989 Sum_{n>=36} 1/a(n) = 36/35.
%F A010989 Sum_{n>=36} (-1)^n/a(n) = A001787(36)*log(2) - A242091(36)/35! = 1236950581248*log(2) - 429895798852508537154517/501401225325 = 0.9742957989... (End)
%p A010989 seq(binomial(n,36),n=36..55); # _Zerinvary Lajos_, Dec 19 2008
%t A010989 Table[Binomial[n,36],{n,36,66}] (* _Vladimir Joseph Stephan Orlovsky_, Apr 26 2011 *)
%o A010989 (Magma) [Binomial(n, 36): n in [36..70]]; // _Vincenzo Librandi_, Jun 12 2013
%Y A010989 Cf. A010986, A010987, A010988, A001787, A242091.
%K A010989 nonn
%O A010989 36,2
%A A010989 _N. J. A. Sloane_