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%I #41 Dec 15 2023 10:41:00
%S 1,30,465,4960,40920,278256,1623160,8347680,38608020,163011640,
%T 635745396,2311801440,7898654920,25518731280,78378960360,229911617056,
%U 646626422970,1749695026860,4568648125690,11541847896480,28277527346376,67327446062800,156077261327400
%N Binomial coefficient C(n,29).
%H T. D. Noe, <a href="/A010982/b010982.txt">Table of n, a(n) for n = 29..1000</a>
%H <a href="/index/Rec#order_30">Index entries for linear recurrences with constant coefficients</a>, signature (30, -435, 4060, -27405, 142506, -593775, 2035800, -5852925, 14307150, -30045015, 54627300, -86493225, 119759850, -145422675, 155117520, -145422675, 119759850, -86493225, 54627300, -30045015, 14307150, -5852925, 2035800, -593775, 142506, -27405, 4060, -435, 30, -1).
%F G.f.: x^29/(1-x)^30. - _Zerinvary Lajos_, Dec 19 2008; adapted to offset by _Enxhell Luzhnica_, Jan 21 2017
%F From _Amiram Eldar_, Dec 12 2020: (Start)
%F Sum_{n>=29} 1/a(n) = 29/28.
%F Sum_{n>=29} (-1)^(n+1)/a(n) = A001787(29)*log(2) - A242091(29)/28! = 7784628224*log(2) - 108340675094713923269/20078358300 = 0.9686369528... (End)
%p seq(binomial(n,29),n=29..53); # _Zerinvary Lajos_, Dec 19 2008
%t Table[Binomial[n,29],{n,29,60}] (* _Vladimir Joseph Stephan Orlovsky_, Apr 26 2011 *)
%o (Magma) [Binomial(n, 29): n in [29..60]]; // _Vincenzo Librandi_, Jun 12 2013
%o (PARI) x='x+O('x^50); Vec(x^29/(1-x)^30) \\ _G. C. Greubel_, Nov 23 2017
%Y Cf. A010980, A010981, A001787, A242091.
%K nonn,easy
%O 29,2
%A _N. J. A. Sloane_
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