A017716 - OEIS

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

%S 1,53,1431,26235,367290,4187106,40475358,341149446,2558620845,

%T 17341763505,107518933731,615790256823,3284214703056,16421073515280,

%U 77413632286320,345780890878896,1469568786235308,5964720367660956

%N Binomial coefficients C(n,52).

%H G. C. Greubel, <a href="/A017716/b017716.txt">Table of n, a(n) for n = 52..10000</a>

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

%F G.f.: x^52/(1-x)^53.

%F E.g.f.: x^52*exp(x)/52!. (End)

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

%F Sum_{n>=52} 1/a(n) = 52/51.

%F Sum_{n>=52} (-1)^n/a(n) = A001787(52)*log(2) - A242091(52)/51! = 117093590311632896*log(2) - 120926939503504532846299231985163098 / 1489925242425959955 = 0.9817952764... (End)

%t Table[Binomial[n,52],{n,52,80}] (* _Vladimir Joseph Stephan Orlovsky_, May 16 2011 *)

%o (Sage) [binomial(n, 52) for n in range(52,70)] # _Zerinvary Lajos_, May 23 2009

%o (PARI) for(n=52, 80, print1(binomial(n,52), ", ")) \\ _G. C. Greubel_, Nov 03 2018

%o (Magma) [Binomial(n,52): n in [52..80]]; // _G. C. Greubel_, Nov 03 2018

%Y Cf. A017713, A017715, A001787, A242091.

%K nonn

%O 52,2

%A _N. J. A. Sloane_