A017761 Binomial coefficients C(n,97).

1, 98, 4851, 161700, 4082925, 83291670, 1429840335, 21243342120, 278818865325, 3283866636050, 35137373005735, 344985116783580, 3133614810784185, 26515202245096950, 210227674943268675, 1569699972909739440, 11086006058675034795, 74341452393467880390

Offset: 97

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• Michael De Vlieger, Table of n, a(n) for n = 97..10000

Crossrefs

Cf. A017762, A001787, A242091.

Programs

Magma

[Binomial(n,97): n in [97..110]]; // G. C. Greubel, Nov 12 2018

Mathematica

Table[Binomial[n, 97], {n, 97, 120}] (* Vladimir Joseph Stephan Orlovsky, Jul 15 2011 *)

PARI

a(n)=binomial(n,97) \\ Charles R Greathouse IV, Jun 28 2012

Sage

[binomial(n, 97) for n in range(97,112)] # Zerinvary Lajos, May 23 2009

Formula

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

G.f.: x^97/(1-x)^98.

E.g.f.: x^97*exp(x)/97!. (End)

From Amiram Eldar, Dec 20 2020: (Start)

Sum_{n>=97} 1/a(n) = 97/96.

Sum_{n>=97} (-1)^(n+1)/a(n) = A001787(97)*log(2) - A242091(97)/96! = 7685131763883640746573763182592*log(2) - 1914409165727592211172313915606620151912614909652567393556011239640929 / 359383377472744727652236128532537647200 = 0.9899961107... (End)