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

50,2

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

Crossrefs

Cf. A001787, A242091.

Sequence in context: A172639 A231648 A017767 * A202044 A238319 A014943

Adjacent sequences: A017711 A017712 A017713 * A017715 A017716 A017717

Keyword

nonn

Author

N. J. A. Sloane

Status

approved