A017747 - OEIS

%I #26 Sep 08 2022 08:44:43

%S 1,84,3570,102340,2225895,39175752,581106988,7471375560,84986896995,

%T 868754947060,8079421007658,69042324974532,546585072715045,

%U 4036320536972640,27965935149024720,182710776306961504

%N Binomial coefficients C(n,83).

%H Michael De Vlieger, <a href="/A017747/b017747.txt">Table of n, a(n) for n = 83..10000</a>

%F From _G. C. Greubel_, Nov 10 2018: (Start)

%F G.f.: x^83/(1-x)^84.

%F E.g.f.: x^83*exp(x)/83!. (End)

%F From _Amiram Eldar_, Dec 18 2020: (Start)

%F Sum_{n>=83} 1/a(n) = 83/82.

%F Sum_{n>=83} (-1)^(n+1)/a(n) = A001787(83)*log(2) - A242091(83)/82! = 401363372112056886002450432*log(2) - 1691854838361747589846883689013163648779313031899544168425629 / 6081348610273871795929269807305700 = 0.9883660041... (End)

%p seq(binomial(n,83),n=83..100); # _Muniru A Asiru_, Nov 11 2018

%t Binomial[Range[83,100],83] (* _Harvey P. Dale_, Oct 08 2016 *)

%o (Sage) [binomial(n, 83) for n in range(83,99)] # _Zerinvary Lajos_, May 23 2009

%o (PARI) for(n=83, 100, print1(binomial(n,83), ", ")) \\ _G. C. Greubel_, Nov 10 2018

%o (Magma) [Binomial(n,83): n in [83..100]]; // _G. C. Greubel_, Nov 10 2018

%o (GAP) List([83..100], n->Binomial(n,83)); # _Muniru A Asiru_, Nov 11 2018

%Y Cf. A001787, A242091.

%K nonn

%O 83,2

%A _N. J. A. Sloane_