A017754 Binomial coefficients C(n,90).

1, 91, 4186, 129766, 3049501, 57940519, 927048304, 12846240784, 157366449604, 1731030945644, 17310309456440, 158940114100040, 1350990969850340, 10704005376506540, 79515468511191440, 556608279578340080

Offset: 90

Author

N. J. A. Sloane

Keywords

• nonn

Links

• Michael De Vlieger, Table of n, a(n) for n = 90..10000

Crossrefs

Cf. A001787, A242091.

Programs

Magma

[Binomial(n,90): n in [90..110]]; // G. C. Greubel, Nov 12 2018

Mathematica

Array[Binomial[#, 90] &, 16, 90] (* Michael De Vlieger, Jul 06 2018 *)

PARI

for(n=90, 110, print1(binomial(n,90), ", ")) \\ G. C. Greubel, Nov 12 2018

Sage

[binomial(n, 90) for n in range(90,106)] # Zerinvary Lajos, May 23 2009

Formula

From G. C. Greubel, Nov 12 2018: (Start)

G.f.: x^90/(1-x)^91.

E.g.f.: x^90*exp(x)/90!. (End)

From Amiram Eldar, Dec 20 2020: (Start)

Sum_{n>=90} 1/a(n) = 90/89.

Sum_{n>=90} (-1)^n/a(n) = A001787(90)*log(2) - A242091(90)/89! = 55707301767842112370460590080*log(2) - 19273610318617028543535699053216921237020997586282137829762590933 / 499143579823256566183661289628524510 = 0.9892424860... (End)