A017713 Binomial coefficients C(n,49).

1, 50, 1275, 22100, 292825, 3162510, 28989675, 231917400, 1652411475, 10648873950, 62828356305, 342700125300, 1742058970275, 8308281242850, 37387265592825, 159518999862720, 648045936942300, 2515943049305400

Offset: 49

Author

N. J. A. Sloane

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 49..10000

Crossrefs

Cf. A011000, A011001, A001787, A242091.

Programs

Magma

[Binomial(n,49): n in [49..80]]; // G. C. Greubel, Nov 03 2018

Mathematica

Table[Binomial[n,49],{n,49,77}] (* Vladimir Joseph Stephan Orlovsky, May 16 2011 *)

PARI

for(n=49, 80, print1(binomial(n,49), ", ")) \\ G. C. Greubel, Nov 03 2018

Python

A017713_list, m = [], [1]*50
for _ in range(10**2):
    A017713_list.append(m[-1])
    for i in range(49):
        m[i+1] += m[i] # Chai Wah Wu, Jan 24 2016

Sage

[binomial(n, 49) for n in range(49,67)] # Zerinvary Lajos, May 23 2009

Formula

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

G.f.: x^49/(1-x)^50.

E.g.f.: x^49*exp(x)/49!. (End)

From Amiram Eldar, Dec 16 2020: (Start)

Sum_{n>=49} 1/a(n) = 49/48.

Sum_{n>=49} (-1)^(n+1)/a(n) = A001787(49)*log(2) - A242091(49)/48! = 13792273858822144*log(2) - 302317348758761304758836609908210929 / 31622903104550986800 = 0.9807421943... (End)