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

49,2

Links

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

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)

Mathematica

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

Prog

(Sage) [binomial(n, 49) for n in range(49, 67)] # Zerinvary Lajos, May 23 2009
(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
(PARI) for(n=49, 80, print1(binomial(n, 49), ", ")) \\ G. C. Greubel, Nov 03 2018
(Magma) [Binomial(n, 49): n in [49..80]]; // G. C. Greubel, Nov 03 2018

Crossrefs

Cf. A011000, A011001, A001787, A242091.

Sequence in context: A161695 A162205 A162492 * A283311 A031602 A231743

Adjacent sequences: A017710 A017711 A017712 * A017714 A017715 A017716

Keyword

nonn

Author

N. J. A. Sloane

Status

approved