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Binomial coefficients C(n,90).
2

%I #22 Sep 08 2022 08:44:43

%S 1,91,4186,129766,3049501,57940519,927048304,12846240784,157366449604,

%T 1731030945644,17310309456440,158940114100040,1350990969850340,

%U 10704005376506540,79515468511191440,556608279578340080

%N Binomial coefficients C(n,90).

%H Michael De Vlieger, <a href="/A017754/b017754.txt">Table of n, a(n) for n = 90..10000</a>

%F From _G. C. Greubel_, Nov 12 2018: (Start)

%F G.f.: x^90/(1-x)^91.

%F E.g.f.: x^90*exp(x)/90!. (End)

%F From _Amiram Eldar_, Dec 20 2020: (Start)

%F Sum_{n>=90} 1/a(n) = 90/89.

%F Sum_{n>=90} (-1)^n/a(n) = A001787(90)*log(2) - A242091(90)/89! = 55707301767842112370460590080*log(2) - 19273610318617028543535699053216921237020997586282137829762590933 / 499143579823256566183661289628524510 = 0.9892424860... (End)

%t Array[Binomial[#, 90] &, 16, 90] (* _Michael De Vlieger_, Jul 06 2018 *)

%o (Sage) [binomial(n, 90) for n in range(90,106)] # _Zerinvary Lajos_, May 23 2009

%o (PARI) for(n=90, 110, print1(binomial(n,90), ", ")) \\ _G. C. Greubel_, Nov 12 2018

%o (Magma) [Binomial(n,90): n in [90..110]]; // _G. C. Greubel_, Nov 12 2018

%Y Cf. A001787, A242091.

%K nonn

%O 90,2

%A _N. J. A. Sloane_