A017714 Binomial coefficients C(n,50).

1, 51, 1326, 23426, 316251, 3478761, 32468436, 264385836, 1916797311, 12565671261, 75394027566, 418094152866, 2160153123141, 10468434365991, 47855699958816, 207374699821536, 855420636763836, 3371363686069236, 12736262814039336, 46252743903616536

Offset: 50

Author

N. J. A. Sloane

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 50..10000

Crossrefs

Cf. A001787, A242091.

Programs

Magma

[Binomial(n,50): n in [50..80]]; // G. C. Greubel, Nov 03 2018

Mathematica

Table[Binomial[n, 50], {n, 50, 5!}] (* Vladimir Joseph Stephan Orlovsky, Sep 25 2008 *)

PARI

for(n=50, 80, print1(binomial(n,50), ", ")) \\ G. C. Greubel, Nov 03 2018

Python

A017714_list, m = [], [1]*51
for _ in range(10**2):
    A017714_list.append(m[-1])
    for i in range(50):
        m[i+1] += m[i] # Chai Wah Wu, Jan 24 2016

Sage

[binomial(n, 50) for n in range(50,68)] # Zerinvary Lajos, May 23 2009

Formula

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

G.f.: x^50/(1-x)^51.

E.g.f.: x^50*exp(x)/50!. (End)

From Amiram Eldar, Dec 16 2020: (Start)

Sum_{n>=50} 1/a(n) = 50/49.

Sum_{n>=50} (-1)^n/a(n) = A001787(50)*log(2) - A242091(50)/49! = 28147497671065600*log(2) - 302317348758761320570288162183704329 / 15495222521229983532 = 0.9811065191... (End)