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A017713 Binomial coefficients C(n,49).

%I A017713 #31 Sep 08 2022 08:44:43
%S A017713 1,50,1275,22100,292825,3162510,28989675,231917400,1652411475,
%T A017713 10648873950,62828356305,342700125300,1742058970275,8308281242850,
%U A017713 37387265592825,159518999862720,648045936942300,2515943049305400
%N A017713 Binomial coefficients C(n,49).
%H A017713 G. C. Greubel, <a href="/A017713/b017713.txt">Table of n, a(n) for n = 49..10000</a>
%F A017713 From _G. C. Greubel_, Nov 03 2018: (Start)
%F A017713 G.f.: x^49/(1-x)^50.
%F A017713 E.g.f.: x^49*exp(x)/49!. (End)
%F A017713 From _Amiram Eldar_, Dec 16 2020: (Start)
%F A017713 Sum_{n>=49} 1/a(n) = 49/48.
%F A017713 Sum_{n>=49} (-1)^(n+1)/a(n) = A001787(49)*log(2) - A242091(49)/48! = 13792273858822144*log(2) - 302317348758761304758836609908210929 / 31622903104550986800 = 0.9807421943... (End)
%t A017713 Table[Binomial[n,49],{n,49,77}] (* _Vladimir Joseph Stephan Orlovsky_, May 16 2011 *)
%o A017713 (Sage) [binomial(n, 49) for n in range(49,67)] # _Zerinvary Lajos_, May 23 2009
%o A017713 (Python)
%o A017713 A017713_list, m = [], [1]*50
%o A017713 for _ in range(10**2):
%o A017713     A017713_list.append(m[-1])
%o A017713     for i in range(49):
%o A017713         m[i+1] += m[i] # _Chai Wah Wu_, Jan 24 2016
%o A017713 (PARI) for(n=49, 80, print1(binomial(n,49), ", ")) \\ _G. C. Greubel_, Nov 03 2018
%o A017713 (Magma) [Binomial(n,49): n in [49..80]]; // _G. C. Greubel_, Nov 03 2018
%Y A017713 Cf. A011000, A011001, A001787, A242091.
%K A017713 nonn
%O A017713 49,2
%A A017713 _N. J. A. Sloane_