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Binomial coefficient C(n,39).
5

%I #27 Dec 15 2023 11:01:24

%S 1,40,820,11480,123410,1086008,8145060,53524680,314457495,1677106640,

%T 8217822536,37353738800,158753389900,635013559600,2403979904200,

%U 8654327655120,29749251314475,97997533741800,310325523515700,947309492837400,2794563003870330

%N Binomial coefficient C(n,39).

%H T. D. Noe, <a href="/A010992/b010992.txt">Table of n, a(n) for n = 39..1000</a>

%H <a href="/index/Rec#order_40">Index entries for linear recurrences with constant coefficients</a>, signature (40, -780, 9880, -91390, 658008, -3838380, 18643560, -76904685, 273438880, -847660528, 2311801440, -5586853480, 12033222880, -23206929840, 40225345056, -62852101650, 88732378800, -113380261800, 131282408400, -137846528820, 131282408400, -113380261800, 88732378800, -62852101650, 40225345056, -23206929840, 12033222880, -5586853480, 2311801440, -847660528, 273438880, -76904685, 18643560, -3838380, 658008, -91390, 9880, -780, 40, -1).

%F G.f.: x^39/(1-x)^40. - _Zerinvary Lajos_, Dec 19 2008

%F From _Amiram Eldar_, Dec 15 2020: (Start)

%F Sum_{n>=39} 1/a(n) = 39/38.

%F Sum_{n>=39} (-1)^(n+1)/a(n) = A001787(39)*log(2) - A242091(39)/38! = 10720238370816*log(2) - 63624578230235205349866541/8562390155550 = 0.9761396932... (End)

%p seq(binomial(n,39),n=39..57); # _Zerinvary Lajos_, Dec 19 2008

%t Table[Binomial[n,39],{n,39,70}] (* _Vladimir Joseph Stephan Orlovsky_, May 16 2011 *)

%o (Magma) [Binomial(n, 39): n in [39..70]]; // _Vincenzo Librandi_, Jun 12 2013

%Y Cf. A010990, A010991, A001787, A242091.

%K nonn

%O 39,2

%A _N. J. A. Sloane_.