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Binomial coefficients C(n,96).
5

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

%S 1,97,4753,156849,3921225,79208745,1346548665,19813501785,

%T 257575523205,3005047770725,31853506369685,309847743777845,

%U 2788629694000605,23381587434312765,183712472698171725,1359472297966470765,9516306085765295355,63255446334792845595

%N Binomial coefficients C(n,96).

%H Michael De Vlieger, <a href="/A017760/b017760.txt">Table of n, a(n) for n = 96..10000</a>

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

%F G.f.: x^96/(1-x)^97.

%F E.g.f.: x^96*exp(x)/96!. (End)

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

%F Sum_{n>=96} 1/a(n) = 96/95.

%F Sum_{n>=96} (-1)^n/a(n) = A001787(96)*log(2) - A242091(96)/95! = 3802951800684688204490109616128*log(2) - 9868088483131918614290277915496170231743780878869426700864981897216 / 3743576848674424246377459672213933825 = 0.9898949826... (End)

%t Table[Binomial[n, 96], {n, 96, 120}] (* _Vladimir Joseph Stephan Orlovsky_, Jul 15 2011 *)

%o (Sage) [binomial(n, 96) for n in range(96,111)] # _Zerinvary Lajos_, May 23 2009

%o (PARI) a(n)=binomial(n,96) \\ _Charles R Greathouse IV_, Jun 28 2012

%o (Magma) [Binomial(n,96): n in [96..110]]; // _G. C. Greubel_, Nov 12 2018

%Y Cf. A017761, A017762, A001787, A242091.

%K nonn,easy

%O 96,2

%A _N. J. A. Sloane_