A017715 Binomial coefficients C(n,51).

1, 52, 1378, 24804, 341055, 3819816, 36288252, 300674088, 2217471399, 14783142660, 90177170226, 508271323092, 2668424446233, 13136858812224, 60992558771040, 268367258592576, 1123787895356412, 4495151581425648

Offset: 51

Author

N. J. A. Sloane

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 51..10000

Crossrefs

Cf. A001787, A242091.

Programs

Magma

[Binomial(n,51): n in [51..80]]; // G. C. Greubel, Nov 03 2018

Mathematica

Table[Binomial[n,51],{n,51,77}] (* Vladimir Joseph Stephan Orlovsky, May 16 2011 *)

PARI

for(n=51, 80, print1(binomial(n,51), ", ")) \\ G. C. Greubel, Nov 03 2018

Sage

[binomial(n, 51) for n in range(51,69)] # Zerinvary Lajos, May 23 2009

Formula

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

G.f.: x^51/(1-x)^52.

E.g.f.: x^51*exp(x)/51!. (End)

From Amiram Eldar, Dec 16 2020: (Start)

Sum_{n>=51} 1/a(n) = 51/50.

Sum_{n>=51} (-1)^(n+1)/a(n) = A001787(51)*log(2) - A242091(51)/50! = 57420895248973824*log(2) - 60463469751752265663579884559739219 / 1519139462865684660 = 0.9814572990... (End)