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Binomial coefficients C(n,68).
2

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

%S 1,69,2415,57155,1028790,15020334,185250786,1984829850,18855883575,

%T 161322559475,1258315963905,9036996468045,60246643120300,

%U 375382930211100,2198671448379300,12165982014365460,63871405575418665

%N Binomial coefficients C(n,68).

%H Michael De Vlieger, <a href="/A017732/b017732.txt">Table of n, a(n) for n = 68..10000</a>

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

%F G.f.: x^68/(1-x)^69.

%F E.g.f.: x^68*exp(x)/68!. (End)

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

%F Sum_{n>=68} 1/a(n) = 68/67.

%F Sum_{n>=68} (-1)^n/a(n) = A001787(68)*log(2) - A242091(68)/67! = 10035028776097996079104*log(2) - 202565512367285681545841250463735407356215875047 / 29122015159885695560022510 = 0.9859047391... (End)

%t Array[Binomial[#, 68] &, 17, 68] (* _Michael De Vlieger_, Jul 06 2018 *)

%o (Sage) [binomial(n, 68) for n in range(68,85)] # _Zerinvary Lajos_, May 23 2009

%o (PARI) for(n=68, 90, print1(binomial(n,68), ", ")) \\ _G. C. Greubel_, Nov 09 2018

%o (Magma) [Binomial(n,68): n in [68..90]]; // _G. C. Greubel_, Nov 09 2018

%Y Cf. A001787, A242091.

%K nonn

%O 68,2

%A _N. J. A. Sloane_