A017730 Binomial coefficients C(n,66).

1, 67, 2278, 52394, 916895, 13019909, 156238908, 1629348612, 15071474661, 125595622175, 954526728530, 6681687099710, 43430966148115, 263926640438545, 1508152231077400, 8144022047817960, 41738112995067045

Offset: 66

Author

N. J. A. Sloane

Keywords

• nonn

Links

• Michael De Vlieger, Table of n, a(n) for n = 66..10000

Crossrefs

Cf. A001787, A242091.

Programs

Magma

[Binomial(n,66): n in [66..90]]; // G. C. Greubel, Nov 08 2018

Mathematica

Binomial[Range[66,86],66] (* Harvey P. Dale, Dec 25 2011 *)

PARI

for(n=66, 90, print1(binomial(n,66), ", ")) \\ G. C. Greubel, Nov 08 2018

Sage

[binomial(n, 66) for n in range(66,83)] # Zerinvary Lajos, May 23 2009

Formula

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

G.f.: x^66/(1-x)^67.

E.g.f.: x^66*exp(x)/66!. (End)

From Amiram Eldar, Dec 17 2020: (Start)

Sum_{n>=66} 1/a(n) = 66/65.

Sum_{n>=66} (-1)^n/a(n) = A001787(66)*log(2) - A242091(66)/65! = 2434970217729660813312*log(2) - 3023365856228144500682860967025333056122272941 / 1791313460761851920471760 = 0.9854955419... (End)