A017746 - OEIS

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

%S 1,83,3486,98770,2123555,36949857,541931236,6890268572,77515521435,

%T 783768050065,7210666060598,60962903966874,477542747740513,

%U 3489735464257595,23929614612052080,154744841157936784

%N Binomial coefficients C(n,82).

%H Michael De Vlieger, <a href="/A017746/b017746.txt">Table of n, a(n) for n = 82..10000</a>

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

%F G.f.: x^82/(1-x)^83.

%F E.g.f.: x^82*exp(x)/82!. (End)

%F From _Amiram Eldar_, Dec 18 2020: (Start)

%F Sum_{n>=82} 1/a(n) = 82/81.

%F Sum_{n>=82} (-1)^n/a(n) = A001787(82)*log(2) - A242091(82)/81! = 198263834416799184651812864*log(2) - 20383793233274067347552815456116292175605687562978728740013 / 148325575860338336486079751397700 = 0.9882289899... (End)

%t Array[Binomial[#, 82] &, 16, 82] (* _Michael De Vlieger_, Jul 06 2018 *)

%o (Sage) [binomial(n, 82) for n in range(82,98)] # _Zerinvary Lajos_, May 23 2009

%o (PARI) for(n=82, 100, print1(binomial(n,82), ", ")) \\ _G. C. Greubel_, Nov 09 2018

%o (Magma) [Binomial(n,82): n in [82..100]]; // _G. C. Greubel_, Nov 09 2018

%Y Cf. A001787, A242091.

%K nonn

%O 82,2

%A _N. J. A. Sloane_