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Binomial coefficients C(n,70).
2

%I #22 Sep 08 2022 08:44:43

%S 1,71,2556,62196,1150626,17259390,218618940,2404808340,23446881315,

%T 205811513765,1646492110120,12124169174520,82848489359220,

%U 528955739755020,3173734438530120,17984495151670680

%N Binomial coefficients C(n,70).

%H Michael De Vlieger, <a href="/A017734/b017734.txt">Table of n, a(n) for n = 70..10000</a>

%F From _G. C. Greubel_, Nov 09 2018: (Start)

%F G.f.: x^70/(1-x)^71.

%F E.g.f.: x^70*exp(x)/70!. (End)

%F From _Amiram Eldar_, Dec 17 2020: (Start)

%F Sum_{n>=70} 1/a(n) = 70/69.

%F Sum_{n>=70} (-1)^n/a(n) = A001787(70)*log(2) - A242091(70)/69! = 41320706725109395619840*log(2) - 202565512367285681545862986460557640882612123732 / 7072489395972240350291181 = 0.9862914664... (End)

%t Array[Binomial[#, 70] &, 16, 70] (* _Michael De Vlieger_, Jul 06 2018 *)

%o (Sage) [binomial(n, 70) for n in range(70,86)] # _Zerinvary Lajos_, May 23 2009

%o (PARI) for(n=70, 90, print1(binomial(n,70), ", ")) \\ _G. C. Greubel_, Nov 09 2018

%o (Magma) [Binomial(n,70): n in [70..90]]; // _G. C. Greubel_, Nov 09 2018

%Y Cf. A001787, A242091.

%K nonn

%O 70,2

%A _N. J. A. Sloane_