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%I #35 Dec 15 2023 15:52:14
%S 1,49,1225,20825,270725,2869685,25827165,202927725,1420494075,
%T 8996462475,52179482355,279871768995,1399358844975,6566222272575,
%U 29078984349975,122131734269895,488526937079580,1867897112363100,6848956078664700,24151581961607100
%N Binomial coefficient C(n,48).
%H T. D. Noe, <a href="/A011001/b011001.txt">Table of n, a(n) for n = 48..1000</a>
%H <a href="/index/Rec#order_49">Index entries for linear recurrences with constant coefficients</a>, signature (49, -1176, 18424, -211876, 1906884, -13983816, 85900584, -450978066, 2054455634, -8217822536, 29135916264, -92263734836, 262596783764, -675248872536, 1575580702584, -3348108992991, 6499270398159, -11554258485616, 18851684897584, -28277527346376, 39049918716424, -49699896548176, 58343356817424, -63205303218876, 63205303218876, -58343356817424, 49699896548176, -39049918716424, 28277527346376, -18851684897584, 11554258485616, -6499270398159, 3348108992991, -1575580702584, 675248872536, -262596783764, 92263734836, -29135916264, 8217822536, -2054455634, 450978066, -85900584, 13983816, -1906884, 211876, -18424, 1176, -49, 1).
%F G.f.: x^48/(1-x)^49. - _Zerinvary Lajos_, Dec 20 2008
%F From _Amiram Eldar_, Dec 15 2020: (Start)
%F Sum_{n>=48} 1/a(n) = 48/47.
%F Sum_{n>=48} (-1)^n/a(n) = A001787(48)*log(2) - A242091(48)/47! = 6755399441055744*log(2) - 21594096339911519462651644572315136 / 4611673369413685575 = 0.9803635237... (End)
%p seq(binomial(n,48),n=48..67); # _Zerinvary Lajos_, Dec 20 2008
%t Table[Binomial[n,48],{n,48,77}] (* _Vladimir Joseph Stephan Orlovsky_, May 16 2011 *)
%o (PARI) a(n)=binomial(n,48) \\ _Charles R Greathouse IV_, Jan 08 2013
%o (Magma) [Binomial(n, 48): n in [48..70]]; // _Vincenzo Librandi_, Jun 12 2013
%o (Python)
%o A011001_list, m = [], [1]*49
%o for _ in range(10**2):
%o A011001_list.append(m[-1])
%o for i in range(48):
%o m[i+1] += m[i] # _Chai Wah Wu_, Jan 24 2016
%Y Cf. A010999, A011000, A001787, A242091.
%K nonn,easy
%O 48,2
%A _N. J. A. Sloane_
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