A017717 Binomial coefficients C(n,53).

1, 54, 1485, 27720, 395010, 4582116, 45057474, 386206920, 2944827765, 20286591270, 127805525001, 743595781824, 4027810484880, 20448884000160, 97862516286480, 443643407165376, 1913212193400684, 7877932561061640

Offset: 53

Author

N. J. A. Sloane

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 53..10000

Crossrefs

Cf. A017713, A017715, A017716, A001787, A242091.

Programs

Magma

[Binomial(n,53): n in [53..80]]; // G. C. Greubel, Nov 03 2018

Mathematica

Table[Binomial[n,53],{n,53,80}] (* Vladimir Joseph Stephan Orlovsky, May 16 2011 *)

PARI

for(n=53, 80, print1(binomial(n,53), ", ")) \\ G. C. Greubel, Nov 03 2018

Sage

[binomial(n, 53) for n in range(53,71)] # Zerinvary Lajos, May 23 2009

Formula

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

G.f.: x^53/(1-x)^54.

E.g.f.: x^53*exp(x)/53!. (End)

From Amiram Eldar, Dec 16 2020: (Start)

Sum_{n>=53} 1/a(n) = 53/52.

Sum_{n>=53} (-1)^(n+1)/a(n) = A001787(53)*log(2) - A242091(53)/52! = 238690780250636288*log(2) - 12818255587371480560673756439003166003 / 77476112606149917660 = 0.9821211403... (End)