A017729 Binomial coefficients C(n,65).

1, 66, 2211, 50116, 864501, 12103014, 143218999, 1473109704, 13442126049, 110524147514, 828931106355, 5727160371180, 36749279048405, 220495674290430, 1244225590638855, 6635869816740560, 33594090947249085

Offset: 65

Author

N. J. A. Sloane

Keywords

• nonn

Links

• Michael De Vlieger, Table of n, a(n) for n = 65..10000

Crossrefs

Cf. A001787, A242091.

Programs

Magma

[Binomial(n,65): n in [65..90]]; // G. C. Greubel, Nov 08 2018

Mathematica

Array[Binomial[#, 65] &, 17, 65] (* Michael De Vlieger, Jul 06 2018 *)

PARI

for(n=65, 90, print1(binomial(n,65), ", ")) \\ G. C. Greubel, Nov 08 2018

Sage

[binomial(n, 65) for n in range(65,82)] # Zerinvary Lajos, May 23 2009

Formula

From G. C. Greubel, Nov 08 2018: (Start)

G.f.: x^65/(1-x)^66.

E.g.f.: x^65*exp(x)/65!. (End)

From Amiram Eldar, Dec 17 2020: (Start)

Sum_{n>=65} 1/a(n) = 65/64.

Sum_{n>=65} (-1)^(n+1)/a(n) = A001787(65)*log(2) - A242091(65)/64! = 1199038364791120855040*log(2) - 3023365856228144500681042094895944098787640077 / 3637744258777914669265728 = 0.9852818956... (End)