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%I #30 Dec 15 2023 11:00:31
%S 1,39,780,10660,111930,962598,7059052,45379620,260932815,1362649145,
%T 6540715896,29135916264,121399651100,476260169700,1768966344600,
%U 6250347750920,21094923659355,68248282427325,212327989773900,636983969321700,1847253511032930,5189902721473470
%N Binomial coefficient C(n,38).
%H T. D. Noe, <a href="/A010991/b010991.txt">Table of n, a(n) for n = 38..1000</a>
%H <a href="/index/Rec#order_39">Index entries for linear recurrences with constant coefficients</a>, signature (39, -741, 9139, -82251, 575757, -3262623, 15380937, -61523748, 211915132, -635745396, 1676056044, -3910797436, 8122425444, -15084504396, 25140840660, -37711260990, 51021117810, -62359143990, 68923264410, -68923264410, 62359143990, -51021117810, 37711260990, -25140840660, 15084504396, -8122425444, 3910797436, -1676056044, 635745396, -211915132, 61523748, -15380937, 3262623, -575757, 82251, -9139, 741, -39, 1).
%F G.f.: x^38/(1-x)^39. - _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>=38} 1/a(n) = 38/37.
%F Sum_{n>=38} (-1)^n/a(n) = A001787(38)*log(2) - A242091(38)/37! = 5222680231936*log(2) - 31812289115113208816827133/8787716212275 = 0.9755552351... (End)
%p seq(binomial(n,38),n=38..57); # _Zerinvary Lajos_, Dec 19 2008
%t Table[Binomial[n,38],{n,38,66}] (* _Vladimir Joseph Stephan Orlovsky_, Apr 26 2011 *)
%o (Magma) [Binomial(n, 38): n in [38..70]]; // _Vincenzo Librandi_, Jun 12 2013
%Y Cf. A010988, A010989, A010990, A001787, A242091.
%K nonn
%O 38,2
%A _N. J. A. Sloane_
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