A017749 Binomial coefficients C(n,85).

1, 86, 3741, 109736, 2441626, 43949268, 666563898, 8760554088, 101841441273, 1063677275518, 10104934117421, 88188515933856, 712857170465336, 5373846361969456, 38000770702498296, 253338471349988640

Offset: 85

Author

N. J. A. Sloane

Keywords

• nonn

Links

• Michael De Vlieger, Table of n, a(n) for n = 85..10000

Crossrefs

Cf. A001787, A242091.

Programs

GAP

List([85..100], n->Binomial(n,85)); # Muniru A Asiru, Nov 11 2018

Magma

[Binomial(n,85): n in [85..105]]; // G. C. Greubel, Nov 10 2018

Maple

seq(binomial(n,85),n=85..100); # Muniru A Asiru, Nov 11 2018

Mathematica

Array[Binomial[#, 85] &, 16, 85] (* Michael De Vlieger, Jul 06 2018 *)

PARI

for(n=85, 105, print1(binomial(n,85), ", ")) \\ G. C. Greubel, Nov 10 2018

Sage

[binomial(n, 85) for n in range(85,101)] # Zerinvary Lajos, May 23 2009

Formula

From G. C. Greubel, Nov 10 2018: (Start)

G.f.: x^85/(1-x)^86.

E.g.f.: x^85*exp(x)/85!. (End)

From Amiram Eldar, Dec 20 2020: (Start)

Sum_{n>=85} 1/a(n) = 85/84.

Sum_{n>=85} (-1)^(n+1)/a(n) = A001787(85)*log(2) - A242091(85)/84! = 1644139114675895677600399360*log(2) - 6767419353446990359387534774224303418673702374958256693151691 / 5938258054738015988966228164780860 = 0.9886306766... (End)