A017721 - OEIS

%I #29 Sep 08 2022 08:44:43

%S 1,58,1711,34220,521855,6471002,67945521,621216192,5047381560,

%T 37014131440,247994680648,1533058025824,8815083648488,47465835030320,

%U 240719591939480,1155454041309504,5271759063474612,22947657099830664

%N Binomial coefficients C(n,57).

%H Michael De Vlieger, <a href="/A017721/b017721.txt">Table of n, a(n) for n = 57..10000</a>

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

%F G.f.: x^57/(1-x)^58.

%F E.g.f.: x^57*exp(x)/57!. (End)

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

%F Sum_{n>=57} 1/a(n) = 57/56.

%F Sum_{n>=57} (-1)^(n+1)/a(n) = A001787(57)*log(2) - A242091(57)/56! = 4107282860161892352*log(2) - 82036835759177476046959075363324597249 / 28815676969304881656 = 0.9833156265... (End)

%t Binomial[Range[57,75],57] (* _Harvey P. Dale_, Jan 10 2013 *)

%o (Sage) [binomial(n, 57) for n in range(57,75)] # _Zerinvary Lajos_, May 23 2009

%o (Magma) [Binomial(n, 57): n in [57..100]]; // _Vincenzo Librandi_, Feb 01 2018

%o (PARI) for(n=57, 80, print1(binomial(n,57), ", ")) \\ _G. C. Greubel_, Nov 03 2018

%Y Cf. A001787, A242091.

%K nonn

%O 57,2

%A _N. J. A. Sloane_