A017761 - OEIS

%I #28 Sep 08 2022 08:44:43

%S 1,98,4851,161700,4082925,83291670,1429840335,21243342120,

%T 278818865325,3283866636050,35137373005735,344985116783580,

%U 3133614810784185,26515202245096950,210227674943268675,1569699972909739440,11086006058675034795,74341452393467880390

%N Binomial coefficients C(n,97).

%H Michael De Vlieger, <a href="/A017761/b017761.txt">Table of n, a(n) for n = 97..10000</a>

%F From _G. C. Greubel_, Nov 12 2018: (Start)

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

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

%F From _Amiram Eldar_, Dec 20 2020: (Start)

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

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

%t Table[Binomial[n, 97], {n, 97, 120}] (* _Vladimir Joseph Stephan Orlovsky_, Jul 15 2011 *)

%o (Sage) [binomial(n, 97) for n in range(97,112)] # _Zerinvary Lajos_, May 23 2009

%o (PARI) a(n)=binomial(n,97) \\ _Charles R Greathouse IV_, Jun 28 2012

%o (Magma) [Binomial(n,97): n in [97..110]]; // _G. C. Greubel_, Nov 12 2018

%Y Cf. A017762, A001787, A242091.

%K nonn,easy

%O 97,2

%A _N. J. A. Sloane_