A017714 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

50,2

LINKS

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

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)

MATHEMATICA

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

PROG

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

(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

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

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