A017744 Binomial coefficients C(n,80).

1, 81, 3321, 91881, 1929501, 32801517, 470155077, 5843355957, 64276915527, 635627275767, 5720645481903, 47325339895743, 362827605867363, 2595612872743443, 17427686431277403, 110375347398090219

Offset: 80

Author

N. J. A. Sloane

Keywords

• nonn

Links

• Michael De Vlieger, Table of n, a(n) for n = 80..10000

Crossrefs

Cf. A001787, A242091.

Programs

Magma

[Binomial(n,80): n in [80..100]]; // G. C. Greubel, Nov 09 2018

Mathematica

Array[Binomial[#, 80] &, 16, 80] (* Michael De Vlieger, Jul 06 2018 *)

PARI

for(n=80, 100, print1(binomial(n,80), ", ")) \\ G. C. Greubel, Nov 09 2018

Sage

[binomial(n, 80) for n in range(80,96)] # Zerinvary Lajos, May 23 2009

Formula

From G. C. Greubel, Nov 09 2018: (Start)

G.f.: x^80/(1-x)^81.

E.g.f.: x^80*exp(x)/80!. (End)

From Amiram Eldar, Dec 18 2020: (Start)

Sum_{n>=80} 1/a(n) = 80/79.

Sum_{n>=80} (-1)^n/a(n) = A001787(80)*log(2) - A242091(80)/79! = 48357032784585166988247040*log(2) - 3397298872212344557925469166982017642113449232981882085888 / 101355810171231196598821163455095 = 0.9879450412... (End)