A017717 - OEIS

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

%S 1,54,1485,27720,395010,4582116,45057474,386206920,2944827765,

%T 20286591270,127805525001,743595781824,4027810484880,20448884000160,

%U 97862516286480,443643407165376,1913212193400684,7877932561061640

%N Binomial coefficients C(n,53).

%H G. C. Greubel, <a href="/A017717/b017717.txt">Table of n, a(n) for n = 53..10000</a>

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

%F G.f.: x^53/(1-x)^54.

%F E.g.f.: x^53*exp(x)/53!. (End)

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

%F Sum_{n>=53} 1/a(n) = 53/52.

%F Sum_{n>=53} (-1)^(n+1)/a(n) = A001787(53)*log(2) - A242091(53)/52! = 238690780250636288*log(2) - 12818255587371480560673756439003166003 / 77476112606149917660 = 0.9821211403... (End)

%t Table[Binomial[n,53],{n,53,80}] (* _Vladimir Joseph Stephan Orlovsky_, May 16 2011 *)

%o (Sage) [binomial(n, 53) for n in range(53,71)] # _Zerinvary Lajos_, May 23 2009

%o (PARI) for(n=53, 80, print1(binomial(n,53), ", ")) \\ _G. C. Greubel_, Nov 03 2018

%o (Magma) [Binomial(n,53): n in [53..80]]; // _G. C. Greubel_, Nov 03 2018

%Y Cf. A017713, A017715, A017716, A001787, A242091.

%K nonn

%O 53,2

%A _N. J. A. Sloane_