A017716 Binomial coefficients C(n,52).

1, 53, 1431, 26235, 367290, 4187106, 40475358, 341149446, 2558620845, 17341763505, 107518933731, 615790256823, 3284214703056, 16421073515280, 77413632286320, 345780890878896, 1469568786235308, 5964720367660956

Offset: 52

Author

N. J. A. Sloane

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 52..10000

Crossrefs

Cf. A017713, A017715, A001787, A242091.

Programs

Magma

[Binomial(n,52): n in [52..80]]; // G. C. Greubel, Nov 03 2018

Mathematica

Table[Binomial[n,52],{n,52,80}] (* Vladimir Joseph Stephan Orlovsky, May 16 2011 *)

PARI

for(n=52, 80, print1(binomial(n,52), ", ")) \\ G. C. Greubel, Nov 03 2018

Sage

[binomial(n, 52) for n in range(52,70)] # Zerinvary Lajos, May 23 2009

Formula

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

G.f.: x^52/(1-x)^53.

E.g.f.: x^52*exp(x)/52!. (End)

From Amiram Eldar, Dec 16 2020: (Start)

Sum_{n>=52} 1/a(n) = 52/51.

Sum_{n>=52} (-1)^n/a(n) = A001787(52)*log(2) - A242091(52)/51! = 117093590311632896*log(2) - 120926939503504532846299231985163098 / 1489925242425959955 = 0.9817952764... (End)