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%I #27 Dec 15 2023 15:46:31
%S 1,43,946,14190,163185,1533939,12271512,85900584,536878650,3042312350,
%T 15820024220,76223753060,343006888770,1451182990950,5804731963800,
%U 22057981462440,79960182801345,277508869722315,925029565741050,2969831763694950,9206478467454345
%N Binomial coefficient C(n,42).
%C Coordination sequence for 42-dimensional cyclotomic lattice Z[zeta_43].
%H T. D. Noe, <a href="/A010995/b010995.txt">Table of n, a(n) for n = 42..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_43">Index entries for linear recurrences with constant coefficients</a>, signature (43, -903, 12341, -123410, 962598, -6096454, 32224114, -145008513, 563921995, -1917334783, 5752004349, -15338678264, 36576848168, -78378960360, 151532656696, -265182149218, 421171648758, -608359048206, 800472431850, -960566918220, 1052049481860, -1052049481860, 960566918220, -800472431850, 608359048206, -421171648758, 265182149218, -151532656696, 78378960360, -36576848168, 15338678264, -5752004349, 1917334783, -563921995, 145008513, -32224114, 6096454, -962598, 123410, -12341, 903, -43, 1).
%F G.f.: x^42/(1-x)^43. - _Zerinvary Lajos_, Dec 20 2008
%F From _Amiram Eldar_, Dec 15 2020: (Start)
%F Sum_{n>=42} 1/a(n) = 42/41.
%F Sum_{n>=42} (-1)^n/a(n) = A001787(42)*log(2) - A242091(42)/41! = 92358976733184*log(2) - 41737723319039140166101476641/651964850415450 = 0.9777363438... (End)
%p seq(binomial(n,42),n=42..57); # _Zerinvary Lajos_, Dec 20 2008
%t Table[Binomial[n,42],{n,42,70}] (* _Vladimir Joseph Stephan Orlovsky_, May 16 2011 *)
%o (Magma) [Binomial(n, 42): n in [42..70]]; // _Vincenzo Librandi_, Jun 12 2013
%Y Cf. A010992, A010994, A001787, A242091.
%K nonn
%O 42,2
%A _N. J. A. Sloane_.
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