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%I #31 Dec 15 2023 10:59:18
%S 1,38,741,9880,101270,850668,6096454,38320568,215553195,1101716330,
%T 5178066751,22595200368,92263734836,354860518600,1292706174900,
%U 4481381406320,14844575908435,47153358767970,144079707346575,424655979547800,1210269541711230,3342649210440540
%N Binomial coefficient C(n,37).
%H T. D. Noe, <a href="/A010990/b010990.txt">Table of n, a(n) for n = 37..1000</a>
%H <a href="/index/Rec#order_38">Index entries for linear recurrences with constant coefficients</a>, signature (38, -703, 8436, -73815, 501942, -2760681, 12620256, -48903492, 163011640, -472733756, 1203322288, -2707475148, 5414950296, -9669554100, 15471286560, -22239974430, 28781143380, -33578000610, 35345263800, -33578000610, 28781143380, -22239974430, 15471286560, -9669554100, 5414950296, -2707475148, 1203322288, -472733756, 163011640, -48903492, 12620256, -2760681, 501942, -73815, 8436, -703, 38, -1).
%F G.f.: x^37/(1-x)^38. - _Zerinvary Lajos_, Dec 19 2008; adapted to offset by _Enxhell Luzhnica_, Jan 23 2017
%F From _Amiram Eldar_, Dec 15 2020: (Start)
%F Sum_{n>=37} 1/a(n) = 37/36.
%F Sum_{n>=37} (-1)^(n+1)/a(n) = A001787(37)*log(2) - A242091(37)/36! = 2542620639232*log(2) - 31812289115104183594771283/18050444111700 = 0.9749413644... (End)
%p seq(binomial(n,37),n=37..55); # _Zerinvary Lajos_, Dec 19 2008
%t Table[Binomial[n,37],{n,37,66}] (* _Vladimir Joseph Stephan Orlovsky_, Apr 26 2011 *)
%o (Magma) [Binomial(n, 37): n in [37..70]]; // _Vincenzo Librandi_, Jun 12 2013
%Y Cf. A010987, A010988, A010989, A001787, A242091.
%K nonn
%O 37,2
%A _N. J. A. Sloane_
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