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Binomial coefficients C(n,54).
3

%I #32 Sep 08 2022 08:44:43

%S 1,55,1540,29260,424270,5006386,50063860,436270780,3381098545,

%T 23667689815,151473214816,895068996640,4922879481520,25371763481680,

%U 123234279768160,566877686933536,2480089880334220,10358022441395860

%N Binomial coefficients C(n,54).

%H Michael De Vlieger, <a href="/A017718/b017718.txt">Table of n, a(n) for n = 54..10000</a>

%F From _G. C. Greubel_, Nov 03 2018: (Start)

%F G.f.: x^54/(1-x)^55.

%F E.g.f.: x^54*exp(x)/54!. (End)

%F From _Amiram Eldar_, Dec 16 2020: (Start)

%F Sum_{n>=54} 1/a(n) = 54/53.

%F Sum_{n>=54} (-1)^n/a(n) = A001787(54)*log(2) - A242091(54)/53! = 486388759756013568*log(2) - 12818255587371480599411812742078124833 / 38020684890055052185 = 0.9824355313... (End)

%t Binomial[Range[54,80],54] (* _Harvey P. Dale_, Apr 02 2011 *)

%o (Sage) [binomial(n, 54) for n in range(54,72)] # _Zerinvary Lajos_, May 23 2009

%o (Magma) [ Binomial(n, 54): n in [54..180]]; // _Vincenzo Librandi_, Apr 04 2011

%o (PARI) for(n=54, 80, print1(binomial(n,54), ", ")) \\ _G. C. Greubel_, Nov 03 2018

%Y Cf. A001787, A242091.

%K nonn

%O 54,2

%A _N. J. A. Sloane_