%I #24 Sep 08 2022 08:44:43

%S 1,52,1378,24804,341055,3819816,36288252,300674088,2217471399,

%T 14783142660,90177170226,508271323092,2668424446233,13136858812224,

%U 60992558771040,268367258592576,1123787895356412,4495151581425648

%N Binomial coefficients C(n,51).

%H G. C. Greubel, <a href="/A017715/b017715.txt">Table of n, a(n) for n = 51..10000</a>

%F From _G. C. Greubel_, Nov 03 2018: (Start)

%F G.f.: x^51/(1-x)^52.

%F E.g.f.: x^51*exp(x)/51!. (End)

%F From _Amiram Eldar_, Dec 16 2020: (Start)

%F Sum_{n>=51} 1/a(n) = 51/50.

%F Sum_{n>=51} (-1)^(n+1)/a(n) = A001787(51)*log(2) - A242091(51)/50! = 57420895248973824*log(2) - 60463469751752265663579884559739219 / 1519139462865684660 = 0.9814572990... (End)

%t Table[Binomial[n,51],{n,51,77}] (* _Vladimir Joseph Stephan Orlovsky_, May 16 2011 *)

%o (Sage) [binomial(n, 51) for n in range(51,69)] # _Zerinvary Lajos_, May 23 2009

%o (PARI) for(n=51, 80, print1(binomial(n,51), ", ")) \\ _G. C. Greubel_, Nov 03 2018

%o (Magma) [Binomial(n,51): n in [51..80]]; // _G. C. Greubel_, Nov 03 2018

%Y Cf. A001787, A242091.

%K nonn

%O 51,2

%A _N. J. A. Sloane_