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Binomial coefficients C(n,66).
2

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

%S 1,67,2278,52394,916895,13019909,156238908,1629348612,15071474661,

%T 125595622175,954526728530,6681687099710,43430966148115,

%U 263926640438545,1508152231077400,8144022047817960,41738112995067045

%N Binomial coefficients C(n,66).

%H Michael De Vlieger, <a href="/A017730/b017730.txt">Table of n, a(n) for n = 66..10000</a>

%F From _G. C. Greubel_, Nov 08 2018: (Start)

%F G.f.: x^66/(1-x)^67.

%F E.g.f.: x^66*exp(x)/66!. (End)

%F From _Amiram Eldar_, Dec 17 2020: (Start)

%F Sum_{n>=66} 1/a(n) = 66/65.

%F Sum_{n>=66} (-1)^n/a(n) = A001787(66)*log(2) - A242091(66)/65! = 2434970217729660813312*log(2) - 3023365856228144500682860967025333056122272941 / 1791313460761851920471760 = 0.9854955419... (End)

%t Binomial[Range[66,86],66] (* _Harvey P. Dale_, Dec 25 2011 *)

%o (Sage) [binomial(n, 66) for n in range(66,83)] # _Zerinvary Lajos_, May 23 2009

%o (PARI) for(n=66, 90, print1(binomial(n,66), ", ")) \\ _G. C. Greubel_, Nov 08 2018

%o (Magma) [Binomial(n,66): n in [66..90]]; // _G. C. Greubel_, Nov 08 2018

%Y Cf. A001787, A242091.

%K nonn

%O 66,2

%A _N. J. A. Sloane_