A017721 Binomial coefficients C(n,57).

1, 58, 1711, 34220, 521855, 6471002, 67945521, 621216192, 5047381560, 37014131440, 247994680648, 1533058025824, 8815083648488, 47465835030320, 240719591939480, 1155454041309504, 5271759063474612, 22947657099830664

Offset: 57

Author

N. J. A. Sloane

Keywords

• nonn

Links

• Michael De Vlieger, Table of n, a(n) for n = 57..10000

Crossrefs

Cf. A001787, A242091.

Programs

Magma

[Binomial(n, 57): n in [57..100]]; // Vincenzo Librandi, Feb 01 2018

Mathematica

Binomial[Range[57,75],57] (* Harvey P. Dale, Jan 10 2013 *)

PARI

for(n=57, 80, print1(binomial(n,57), ", ")) \\ G. C. Greubel, Nov 03 2018

Sage

[binomial(n, 57) for n in range(57,75)] # Zerinvary Lajos, May 23 2009

Formula

From G. C. Greubel, Nov 03 2018: (Start)

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

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

From Amiram Eldar, Dec 16 2020: (Start)

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

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