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A017747 Binomial coefficients C(n,83).

%I A017747 #26 Sep 08 2022 08:44:43
%S A017747 1,84,3570,102340,2225895,39175752,581106988,7471375560,84986896995,
%T A017747 868754947060,8079421007658,69042324974532,546585072715045,
%U A017747 4036320536972640,27965935149024720,182710776306961504
%N A017747 Binomial coefficients C(n,83).
%H A017747 Michael De Vlieger, <a href="/A017747/b017747.txt">Table of n, a(n) for n = 83..10000</a>
%F A017747 From _G. C. Greubel_, Nov 10 2018: (Start)
%F A017747 G.f.: x^83/(1-x)^84.
%F A017747 E.g.f.: x^83*exp(x)/83!. (End)
%F A017747 From _Amiram Eldar_, Dec 18 2020: (Start)
%F A017747 Sum_{n>=83} 1/a(n) = 83/82.
%F A017747 Sum_{n>=83} (-1)^(n+1)/a(n) = A001787(83)*log(2) - A242091(83)/82! = 401363372112056886002450432*log(2) - 1691854838361747589846883689013163648779313031899544168425629 / 6081348610273871795929269807305700 = 0.9883660041... (End)
%p A017747 seq(binomial(n,83),n=83..100); # _Muniru A Asiru_, Nov 11 2018
%t A017747 Binomial[Range[83,100],83] (* _Harvey P. Dale_, Oct 08 2016 *)
%o A017747 (Sage) [binomial(n, 83) for n in range(83,99)] # _Zerinvary Lajos_, May 23 2009
%o A017747 (PARI) for(n=83, 100, print1(binomial(n,83), ", ")) \\ _G. C. Greubel_, Nov 10 2018
%o A017747 (Magma) [Binomial(n,83): n in [83..100]]; // _G. C. Greubel_, Nov 10 2018
%o A017747 (GAP) List([83..100], n->Binomial(n,83)); # _Muniru A Asiru_, Nov 11 2018
%Y A017747 Cf. A001787, A242091.
%K A017747 nonn
%O A017747 83,2
%A A017747 _N. J. A. Sloane_