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Binomial coefficients C(n,94).
3

%I #26 Sep 08 2022 08:44:43

%S 1,95,4560,147440,3612280,71523144,1192052400,17199613200,

%T 219295068300,2509710226100,26100986351440,249145778809200,

%U 2200787712814600,18114175790089400,139737927523546800,1015428940004440080,6981073962530525550,45582306461228725650

%N Binomial coefficients C(n,94).

%H Michael De Vlieger, <a href="/A017758/b017758.txt">Table of n, a(n) for n = 94..10000</a>

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

%F G.f.: x^94/(1-x)^95.

%F E.g.f.: x^94*exp(x)/94!. (End)

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

%F Sum_{n>=94} 1/a(n) = 94/93.

%F Sum_{n>=94} (-1)^n/a(n) = A001787(94)*log(2) - A242091(94)/93! = 930930909542605966724141416448*log(2) - 154188882548936228348285592429449074905987023631107827159541306779 / 238951713745176015726220830141314925 = 0.9896864636... (End)

%t Table[Binomial[n, 94], {n, 94, 120}] (* _Vladimir Joseph Stephan Orlovsky_, Jul 15 2011 *)

%o (Sage) [binomial(n, 94) for n in range(93,110)] # _Zerinvary Lajos_, May 23 2009

%o (PARI) for(n=94, 110, print1(binomial(n,94), ", ")) \\ _G. C. Greubel_, Nov 12 2018

%o (Magma) [Binomial(n,94): n in [94..110]]; // _G. C. Greubel_, Nov 12 2018

%Y Cf. A017760, A017761, A001787, A242091.

%K nonn

%O 94,2

%A _N. J. A. Sloane_