A017753 - OEIS

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

%S 1,90,4095,125580,2919735,54891018,869107785,11919192480,144520208820,

%T 1573664496040,15579278510796,141629804643600,1192050855750300,

%U 9353014406656200,68811463134684900,477092811067148640

%N Binomial coefficients C(n,89).

%H Michael De Vlieger, <a href="/A017753/b017753.txt">Table of n, a(n) for n = 89..10000</a>

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

%F G.f.: x^89/(1-x)^90.

%F E.g.f.: x^89*exp(x)/89!. (End)

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

%F Sum_{n>=89} 1/a(n) = 89/88.

%F Sum_{n>=89} (-1)^(n+1)/a(n) = A001787(89)*log(2) - A242091(89)/88! = 27544165874099711116505513984*log(2) - 19273610318617028543535699052712169302368266227220008435756217833 / 1009503869305462718124258788012746200 = 0.9891254514... (End)

%t Array[Binomial[#, 89] &, 16, 89] (* _Michael De Vlieger_, Jul 06 2018 *)

%o (Sage) [binomial(n, 89) for n in range(89,105)] # _Zerinvary Lajos_, May 23 2009

%o (PARI) for(n=89, 110, print1(binomial(n,89), ", ")) \\ _G. C. Greubel_, Nov 12 2018

%o (Magma) [Binomial(n,89): n in [89..110]]; // _G. C. Greubel_, Nov 12 2018

%Y Cf. A001787, A242091.

%K nonn

%O 89,2

%A _N. J. A. Sloane_