A017762 Binomial coefficients C(n,98).

1, 99, 4950, 166650, 4249575, 87541245, 1517381580, 22760723700, 301579589025, 3585446225075, 38722819230810, 383707936014390, 3517322746798575, 30032524991895525, 240260199935164200, 1809960172844903640, 12895966231519938435, 87237418624987818825

Offset: 98

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• Michael De Vlieger, Table of n, a(n) for n = 98..10000

Crossrefs

Cf. A001787, A242091.

Programs

Magma

[Binomial(n,98): n in [98..115]]; // G. C. Greubel, Nov 12 2018

Maple

A017762:=n->binomial(n,98); seq(A017762(k), k=98..200); # Wesley Ivan Hurt, Nov 05 2013

Mathematica

Table[Binomial[n, 98], {n, 98, 120}] (* Vladimir Joseph Stephan Orlovsky, Jul 15 2011 *)

PARI

a(n)=binomial(n,98) \\ Charles R Greathouse IV, Jun 28 2012

Sage

[binomial(n, 98) for n in range(98,113)] # Zerinvary Lajos, May 23 2009

Formula

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

G.f.: x^98/(1-x)^99.

E.g.f.: x^98*exp(x)/98!. (End)

From Amiram Eldar, Dec 20 2020: (Start)

Sum_{n>=98} 1/a(n) = 98/97.

Sum_{n>=98} (-1)^n/a(n) = A001787(98)*log(2) - A242091(98)/97! = 15528719852795810168334614265856*log(2) - 1914409165727592211172313915606799843601351282016393511620277508464529 / 177858100075797135623810737079878325400 = 0.9900952340... (End)