A017718 Binomial coefficients C(n,54).

1, 55, 1540, 29260, 424270, 5006386, 50063860, 436270780, 3381098545, 23667689815, 151473214816, 895068996640, 4922879481520, 25371763481680, 123234279768160, 566877686933536, 2480089880334220, 10358022441395860

Offset: 54

Author

N. J. A. Sloane

Keywords

• nonn

Links

• Michael De Vlieger, Table of n, a(n) for n = 54..10000

Crossrefs

Cf. A001787, A242091.

Programs

Magma

[ Binomial(n, 54): n in [54..180]]; // Vincenzo Librandi, Apr 04 2011

Mathematica

Binomial[Range[54,80],54]  (* Harvey P. Dale, Apr 02 2011 *)

PARI

for(n=54, 80, print1(binomial(n,54), ", ")) \\ G. C. Greubel, Nov 03 2018

Sage

[binomial(n, 54) for n in range(54,72)] # Zerinvary Lajos, May 23 2009

Formula

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

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

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

From Amiram Eldar, Dec 16 2020: (Start)

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

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