A017719 Binomial coefficients C(n,55).

1, 56, 1596, 30856, 455126, 5461512, 55525372, 491796152, 3872894697, 27540584512, 179013799328, 1074082795968, 5996962277488, 31368725759168, 154603005527328, 721480692460864, 3201570572795084, 13559593014190944

Offset: 55

Author

N. J. A. Sloane

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 55..10000

Crossrefs

Cf. A001787, A242091.

Programs

Magma

[Binomial(n,55): n in [55..80]]; // G. C. Greubel, Nov 03 2018

Mathematica

Table[Binomial[n,55],{n,55,80}] (* Vladimir Joseph Stephan Orlovsky, May 16 2011 *)

PARI

for(n=55, 80, print1(binomial(n,55), ", ")) \\ G. C. Greubel, Nov 03 2018

Sage

[binomial(n, 55) for n in range(55,73)] # Zerinvary Lajos, May 23 2009

Formula

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

G.f.: x^55/(1-x)^56.

E.g.f.: x^55*exp(x)/55!. (End)

From Amiram Eldar, Dec 16 2020: (Start)

Sum_{n>=55} 1/a(n) = 55/54.

Sum_{n>=55} (-1)^(n+1)/a(n) = A001787(55)*log(2) - A242091(55)/54! = 990791918021509120*log(2) - 25636511174742961236844310374211301851 / 37329399710235869418 = 0.9827390452... (End)