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A017714 Binomial coefficients C(n,50).

%I A017714 #30 Sep 08 2022 08:44:43
%S A017714 1,51,1326,23426,316251,3478761,32468436,264385836,1916797311,
%T A017714 12565671261,75394027566,418094152866,2160153123141,10468434365991,
%U A017714 47855699958816,207374699821536,855420636763836,3371363686069236,12736262814039336,46252743903616536
%N A017714 Binomial coefficients C(n,50).
%H A017714 G. C. Greubel, <a href="/A017714/b017714.txt">Table of n, a(n) for n = 50..10000</a>
%F A017714 From _G. C. Greubel_, Nov 03 2018: (Start)
%F A017714 G.f.: x^50/(1-x)^51.
%F A017714 E.g.f.: x^50*exp(x)/50!. (End)
%F A017714 From _Amiram Eldar_, Dec 16 2020: (Start)
%F A017714 Sum_{n>=50} 1/a(n) = 50/49.
%F A017714 Sum_{n>=50} (-1)^n/a(n) = A001787(50)*log(2) - A242091(50)/49! = 28147497671065600*log(2) - 302317348758761320570288162183704329 / 15495222521229983532 = 0.9811065191... (End)
%t A017714 Table[Binomial[n, 50], {n, 50, 5!}] (* _Vladimir Joseph Stephan Orlovsky_, Sep 25 2008 *)
%o A017714 (Sage) [binomial(n, 50) for n in range(50,68)] # _Zerinvary Lajos_, May 23 2009
%o A017714 (Python)
%o A017714 A017714_list, m = [], [1]*51
%o A017714 for _ in range(10**2):
%o A017714     A017714_list.append(m[-1])
%o A017714     for i in range(50):
%o A017714         m[i+1] += m[i] # _Chai Wah Wu_, Jan 24 2016
%o A017714 (PARI) for(n=50, 80, print1(binomial(n,50), ", ")) \\ _G. C. Greubel_, Nov 03 2018
%o A017714 (Magma) [Binomial(n,50): n in [50..80]]; // _G. C. Greubel_, Nov 03 2018
%Y A017714 Cf. A001787, A242091.
%K A017714 nonn
%O A017714 50,2
%A A017714 _N. J. A. Sloane_