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%I #28 Dec 15 2023 11:03:15
%S 1,42,903,13244,148995,1370754,10737573,73629072,450978066,2505433700,
%T 12777711870,60403728840,266783135710,1108176102180,4353548972850,
%U 16253249498640,57902201338905,197548686920970,647520696018735,2044802197953900,6236646703759395
%N a(n) = binomial coefficient C(n,41).
%H T. D. Noe, <a href="/A010994/b010994.txt">Table of n, a(n) for n = 41..1000</a>
%H <a href="/index/Rec#order_42">Index entries for linear recurrences with constant coefficients</a>, signature (42, -861, 11480, -111930, 850668, -5245786, 26978328, -118030185, 445891810, -1471442973, 4280561376, -11058116888, 25518731280, -52860229080, 98672427616, -166509721602, 254661927156, -353697121050, 446775310800, -513791607420, 538257874440, -513791607420, 446775310800, -353697121050, 254661927156, -166509721602, 98672427616, -52860229080, 25518731280, -11058116888, 4280561376, -1471442973, 445891810, -118030185, 26978328, -5245786, 850668, -111930, 11480, -861, 42, -1).
%F G.f.: x^41/(1-x)^42. - _Zerinvary Lajos_, Dec 20 2008
%F From _Amiram Eldar_, Dec 15 2020: (Start)
%F Sum_{n>=41} 1/a(n) = 41/40.
%F Sum_{n>=41} (-1)^(n+1)/a(n) = A001787(41)*log(2) - A242091(41)/40! = 45079976738816*log(2) - 41737723319038472299669343741/1335732864265800 = 0.9772284535... (End)
%p seq(binomial(n,41),n=41..57); # _Zerinvary Lajos_, Dec 20 2008
%t Table[Binomial[n,41],{n,41,70}] (* _Vladimir Joseph Stephan Orlovsky_, May 16 2011 *)
%o (Magma) [Binomial(n, 41): n in [41..70]]; // _Vincenzo Librandi_, Jun 12 2013
%Y Cf. A010990, A010991, A010992, A001787, A242091.
%K nonn,easy
%O 41,2
%A _N. J. A. Sloane_
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