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Binomial coefficients C(n,88).
2

%I #24 Sep 08 2022 08:44:43

%S 1,89,4005,121485,2794155,51971283,814216767,11050084695,132601016340,

%T 1429144287220,14005614014756,126050526132804,1050421051106700,

%U 8160963550905900,59458448728028700,408281347932463740

%N Binomial coefficients C(n,88).

%H Michael De Vlieger, <a href="/A017752/b017752.txt">Table of n, a(n) for n = 88..10000</a>

%F From _G. C. Greubel_, Nov 12 2018: (Start)

%F G.f.: x^88/(1-x)^89.

%F E.g.f.: x^88*exp(x)/88!. (End)

%F From _Amiram Eldar_, Dec 20 2020: (Start)

%F Sum_{n>=88} 1/a(n) = 88/87.

%F Sum_{n>=88} (-1)^n/a(n) = A001787(88)*log(2) - A242091(88)/87! = 13617340432139183023890366464*log(2) - 108278709655151845750200556470175246057215350235080548404839936 / 11471634878471167251412031681963025 = 0.9890058411... (End)

%t Binomial[Range[88,110],88] (* _Harvey P. Dale_, Mar 24 2013 *)

%o (Sage) [binomial(n, 88) for n in range(88,104)] # _Zerinvary Lajos_, May 23 2009

%o (PARI) for(n=88, 110, print1(binomial(n,88), ", ")) \\ _G. C. Greubel_, Nov 12 2018

%o (Magma) [Binomial(n,88): n in [88..110]]; // _G. C. Greubel_, Nov 12 2018

%Y Cf. A001787, A242091.

%K nonn

%O 88,2

%A _N. J. A. Sloane_