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A011000 a(n) = binomial coefficient C(n,47).

%I A011000 #28 Dec 15 2023 11:09:38
%S A011000 1,48,1176,19600,249900,2598960,22957480,177100560,1217566350,
%T A011000 7575968400,43183019880,227692286640,1119487075980,5166863427600,
%U A011000 22512762077400,93052749919920,366395202809685,1379370175283520,4981058966301600,17302625882942400,57963796707857040
%N A011000 a(n) = binomial coefficient C(n,47).
%H A011000 T. D. Noe, <a href="/A011000/b011000.txt">Table of n, a(n) for n = 47..1000</a>
%H A011000 <a href="/index/Rec#order_48">Index entries for linear recurrences with constant coefficients</a>, signature (48, -1128, 17296, -194580, 1712304, -12271512, 73629072, -377348994, 1677106640, -6540715896, 22595200368, -69668534468, 192928249296, -482320623240, 1093260079344, -2254848913647, 4244421484512, -7309837001104, 11541847896480, -16735679449896, 22314239266528, -27385657281648, 30957699535776, -32247603683100, 30957699535776, -27385657281648, 22314239266528, -16735679449896, 11541847896480, -7309837001104, 4244421484512, -2254848913647, 1093260079344, -482320623240, 192928249296, -69668534468, 22595200368, -6540715896, 1677106640, -377348994, 73629072, -12271512, 1712304, -194580, 17296, -1128, 48, -1).
%F A011000 G.f.: x^47/(1-x)^48. - _Zerinvary Lajos_, Dec 20 2008
%F A011000 From _Amiram Eldar_, Dec 15 2020: (Start)
%F A011000 Sum_{n>=47} 1/a(n) = 47/46.
%F A011000 Sum_{n>=47} (-1)^(n+1)/a(n) = A001787(47)*log(2) - A242091(47)/46! = 3307330976350208*log(2) - 1349631021244469672053597823194021/588724259925151350 = 0.9799696418... (End)
%p A011000 seq(binomial(n,47),n=47..67); # _Zerinvary Lajos_, Dec 20 2008
%t A011000 Table[Binomial[n,47],{n,47,77}] (* _Vladimir Joseph Stephan Orlovsky_, May 16 2011 *)
%o A011000 (Magma) [Binomial(n, 47): n in [47..70]]; // _Vincenzo Librandi_, Jun 12 2013
%Y A011000 Cf. A010998, A010999, A001787, A242091.
%K A011000 nonn
%O A011000 47,2
%A A011000 _N. J. A. Sloane_