login
Binomial coefficients C(n,61).
2

%I #25 Sep 08 2022 08:44:43

%S 1,62,1953,41664,677040,8936928,99795696,969443904,8361453672,

%T 65033528560,461738052776,3022285436352,18385569737808,

%U 104656320045984,560658857389200,2840671544105280,13670731806006660

%N Binomial coefficients C(n,61).

%H Michael De Vlieger, <a href="/A017725/b017725.txt">Table of n, a(n) for n = 61..10000</a>

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

%F G.f.: x^61/(1-x)^62.

%F E.g.f.: x^61*exp(x)/61!. (End)

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

%F Sum_{n>=61} 1/a(n) = 61/60.

%F Sum_{n>=61} (-1)^(n+1)/a(n) = A001787(61)*log(2) - A242091(61)/60! = 70328211781017665536*log(2) - 11810022875891189455560842652264706707798107 / 242267804119430792522820 = 0.9843603731... (End)

%t With[{x = 61}, Binomial[Range[x, x + 16], x]] (* _Michael De Vlieger_, Jan 31 2018 *)

%o (Sage) [binomial(n, 61) for n in range(61,78)] # _Zerinvary Lajos_, May 23 2009

%o (PARI) for(n=61, 80, print1(binomial(n,61), ", ")) \\ _G. C. Greubel_, Nov 03 2018

%o (Magma) [Binomial(n,61): n in [61..80]]; // _G. C. Greubel_, Nov 03 2018

%Y Cf. A001787, A242091.

%K nonn

%O 61,2

%A _N. J. A. Sloane_