A017753 Binomial coefficients C(n,89).

1, 90, 4095, 125580, 2919735, 54891018, 869107785, 11919192480, 144520208820, 1573664496040, 15579278510796, 141629804643600, 1192050855750300, 9353014406656200, 68811463134684900, 477092811067148640

Offset: 89

Author

N. J. A. Sloane

Keywords

• nonn

Links

• Michael De Vlieger, Table of n, a(n) for n = 89..10000

Crossrefs

Cf. A001787, A242091.

Programs

Magma

[Binomial(n,89): n in [89..110]]; // G. C. Greubel, Nov 12 2018

Mathematica

Array[Binomial[#, 89] &, 16, 89] (* Michael De Vlieger, Jul 06 2018 *)

PARI

for(n=89, 110, print1(binomial(n,89), ", ")) \\ G. C. Greubel, Nov 12 2018

Sage

[binomial(n, 89) for n in range(89,105)] # Zerinvary Lajos, May 23 2009

Formula

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

G.f.: x^89/(1-x)^90.

E.g.f.: x^89*exp(x)/89!. (End)

From Amiram Eldar, Dec 20 2020: (Start)

Sum_{n>=89} 1/a(n) = 89/88.

Sum_{n>=89} (-1)^(n+1)/a(n) = A001787(89)*log(2) - A242091(89)/88! = 27544165874099711116505513984*log(2) - 19273610318617028543535699052712169302368266227220008435756217833 / 1009503869305462718124258788012746200 = 0.9891254514... (End)