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Binomial coefficients C(n,64).
2

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

%S 1,65,2145,47905,814385,11238513,131115985,1329890705,11969016345,

%T 97082021465,718406958841,4898229264825,31022118677225,

%U 183746395242025,1023729916348425,5391644226101705,26958221130508525

%N Binomial coefficients C(n,64).

%H Michael De Vlieger, <a href="/A017728/b017728.txt">Table of n, a(n) for n = 64..10000</a>

%F From _G. C. Greubel_, Nov 08 2018: (Start)

%F G.f.: x^64/(1-x)^65.

%F E.g.f.: x^64*exp(x)/64!. (End)

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

%F Sum_{n>=64} 1/a(n) = 64/63.

%F Sum_{n>=64} (-1)^n/a(n) = A001787(64)*log(2) - A242091(64)/63! = 590295810358705651712*log(2) - 1511682928114072250338673755441561389600833536 / 3694584012821319585973005 = 0.9850618563... (End)

%t Array[Binomial[#, 64] &, 17, 64] (* _Michael De Vlieger_, Jul 06 2018 *)

%o (Sage) [binomial(n, 64) for n in range(64,81)] # _Zerinvary Lajos_, May 23 2009

%o (PARI) for(n=64, 90, print1(binomial(n,64), ", ")) \\ _G. C. Greubel_, Nov 08 2018

%o (Magma) [Binomial(n,64): n in [64..90]]; // _G. C. Greubel_, Nov 08 2018

%Y Cf. A001787, A242091.

%K nonn

%O 64,2

%A _N. J. A. Sloane_