A017729 Binomial coefficients C(n,65).

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

Offset

65,2

Links

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

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)

Mathematica

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

Prog

(Sage) [binomial(n, 65) for n in range(65, 82)] # Zerinvary Lajos, May 23 2009
(PARI) for(n=65, 90, print1(binomial(n, 65), ", ")) \\ G. C. Greubel, Nov 08 2018
(Magma) [Binomial(n, 65): n in [65..90]]; // G. C. Greubel, Nov 08 2018

Crossrefs

Cf. A001787, A242091.

Sequence in context: A035728 A114252 A240464 * A230993 A173124 A004365

Adjacent sequences: A017726 A017727 A017728 * A017730 A017731 A017732

Keyword

nonn

Author

N. J. A. Sloane

Status

approved