A017763 a(n) = binomial coefficient C(n,99).

1, 100, 5050, 171700, 4421275, 91962520, 1609344100, 24370067800, 325949656825, 3911395881900, 42634215112710, 426342151127100, 3943664897925675, 33976189889821200, 274236389824985400

Offset: 99

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 99..10000

Crossrefs

Cf. A001787, A242091.

Programs

Magma

[Binomial(n,99): n in [99..120]]; // G. C. Greubel, Nov 12 2018

Mathematica

Table[Binomial[n,99],{n,99,5!}] (* Vladimir Joseph Stephan Orlovsky, Dec 25 2008 *)

PARI

a(n)=binomial(n,99) \\ Charles R Greathouse IV, Jun 28 2012

Sage

[binomial(n, 99) for n in range(99,114)] # Zerinvary Lajos, May 23 2009

Formula

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

G.f.: x^99/(1-x)^100.

E.g.f.: x^99*exp(x)/99!. (End)

From Amiram Eldar, Dec 20 2020: (Start)

Sum_{n>=99} 1/a(n) = 99/98.

Sum_{n>=99} (-1)^(n+1)/a(n) = A001787(99)*log(2) - A242091(99)/98! = 31374352355648677687043404333056*log(2) - 1914409165727592211172313915606888772651389180584205416988817447627229 / 88030776805192521672391172898121595400 = 0.9901924115... (End)