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a(n) = binomial coefficient C(n,46).
5

%I #34 Dec 15 2023 15:48:24

%S 1,47,1128,18424,230300,2349060,20358520,154143080,1040465790,

%T 6358402050,35607051480,184509266760,891794789340,4047376351620,

%U 17345898649800,70539987842520,273342452889765,1012974972473835,3601688791018080,12321566916640800,40661170824914640

%N a(n) = binomial coefficient C(n,46).

%C Coordination sequence for 46-dimensional cyclotomic lattice Z[zeta_47].

%H T. D. Noe, <a href="/A010999/b010999.txt">Table of n, a(n) for n = 46..1000</a>

%H Matthias Beck and Serkan Hosten, <a href="http://arxiv.org/abs/math/0508136">Cyclotomic polytopes and growth series of cyclotomic lattices</a>, arXiv:math/0508136 [math.CO], 2005-2006.

%H <a href="/index/Rec#order_47">Index entries for linear recurrences with constant coefficients</a>, signature (47, -1081, 16215, -178365, 1533939, -10737573, 62891499, -314457495, 1362649145, -5178066751, 17417133617, -52251400851, 140676848445, -341643774795, 751616304549, -1503232609098, 2741188875414, -4568648125690, 6973199770790, -9762479679106, 12551759587422, -14833897694226, 16123801841550, -16123801841550, 14833897694226, -12551759587422, 9762479679106, -6973199770790, 4568648125690, -2741188875414, 1503232609098, -751616304549, 341643774795, -140676848445, 52251400851, -17417133617, 5178066751, -1362649145, 314457495, -62891499, 10737573, -1533939, 178365, -16215, 1081, -47, 1).

%F G.f.: x^46/(1-x)^47. - _Zerinvary Lajos_, Dec 20 2008

%F From _Amiram Eldar_, Dec 15 2020: (Start)

%F Sum_{n>=46} 1/a(n) = 46/45.

%F Sum_{n>=46} (-1)^n/a(n) = A001787(46)*log(2) - A242091(46)/45! = 1618481116086272*log(2) - 14357776821749670963095578951159/12798353476633725 = 0.9795596119... (End)

%p seq(binomial(n,46),n=46..67); # _Zerinvary Lajos_, Dec 20 2008

%t Table[Binomial[n,46],{n,46,77}] (* _Vladimir Joseph Stephan Orlovsky_, May 16 2011 *)

%o (Magma) [Binomial(n, 46): n in [46..70]]; // _Vincenzo Librandi_, Jun 12 2013

%Y Cf. A010997, A010998, A001787, A242091.

%K nonn

%O 46,2

%A _N. J. A. Sloane_