A017748 - OEIS

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

%S 1,85,3655,105995,2331890,41507642,622614630,8093990190,93080887185,

%T 961835834245,9041256841903,78083581816435,624668654531480,

%U 4660989191504120,32626924340528840,215337700647490344

%N Binomial coefficients C(n,84).

%H Michael De Vlieger, <a href="/A017748/b017748.txt">Table of n, a(n) for n = 84..10000</a>

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

%F G.f.: x^84/(1-x)^85.

%F E.g.f.: x^84*exp(x)/84!. (End)

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

%F Sum_{n>=84} 1/a(n) = 84/83.

%F Sum_{n>=84} (-1)^n/a(n) = A001787(84)*log(2) - A242091(84)/83! = 812398150781030805402550272*log(2) - 3383709676723495179693767384107675907832497859728358144156958 / 6008951603008706655501540404837775 = 0.9884998637... (End)

%p seq(binomial(n,84),n=84..100); # _Muniru A Asiru_, Nov 11 2018

%t Array[Binomial[#, 84] &, 16, 84] (* _Michael De Vlieger_, Jul 06 2018 *)

%o (Sage) [binomial(n, 84) for n in range(84,100)] # _Zerinvary Lajos_, May 23 2009

%o (PARI) for(n=84, 105, print1(binomial(n,84), ", ")) \\ _G. C. Greubel_, Nov 10 2018

%o (Magma) [Binomial(n,84): n in [84..105]]; // _G. C. Greubel_, Nov 10 2018

%o (GAP) List([84..100], n->Binomial(n,84)); # _Muniru A Asiru_, Nov 11 2018

%Y Cf. A001787, A242091.

%K nonn

%O 84,2

%A _N. J. A. Sloane_