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%I #33 Dec 15 2023 10:47:09
%S 1,35,630,7770,73815,575757,3838380,22481940,118030185,563921995,
%T 2481256778,10150595910,38910617655,140676848445,482320623240,
%U 1575580702584,4923689695575,14771069086725,42671977361650,119032357903550,321387366339585,841728816603675
%N Binomial coefficient C(n,34).
%H T. D. Noe, <a href="/A010987/b010987.txt">Table of n, a(n) for n = 34..1000</a>
%H <a href="/index/Rec#order_35">Index entries for linear recurrences with constant coefficients</a>, signature (35, -595, 6545, -52360, 324632, -1623160, 6724520, -23535820, 70607460, -183579396, 417225900, -834451800, 1476337800, -2319959400, 3247943160, -4059928950, 4537567650, -4537567650, 4059928950, -3247943160, 2319959400, -1476337800, 834451800, -417225900, 183579396, -70607460, 23535820, -6724520, 1623160, -324632, 52360, -6545, 595, -35, 1).
%F G.f.: x^34/(1-x)^35 . - _Zerinvary Lajos_, Dec 19 2008; adapted to offset by _Enxhell Luzhnica_, Jan 23 2017
%F From _Amiram Eldar_, Dec 12 2020: (Start)
%F Sum_{n>=34} 1/a(n) = 34/33.
%F Sum_{n>=34} (-1)^n/a(n) = A001787(34)*log(2) - A242091(34)/33! = 292057776128*log(2) - 429895798850931019349797/2123581660200 = 0.9728992064... (End)
%p seq(binomial(n,34),n=34..55); # _Zerinvary Lajos_, Dec 19 2008
%t Table[Binomial[n,34],{n,34,60}] (* _Vladimir Joseph Stephan Orlovsky_, Apr 26 2011 *)
%o (Magma) [Binomial(n, 34): n in [34..70]]; // _Vincenzo Librandi_, Jun 12 2013
%o (PARI) x='x+O('x^50); Vec(x^34/(1-x)^35) \\ _G. C. Greubel_, Nov 23 2017
%Y Cf. A010984, A010985, A010986, A001787, A242091.
%K nonn
%O 34,2
%A _N. J. A. Sloane_
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