# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a010999 Showing 1-1 of 1 %I A010999 #34 Dec 15 2023 15:48:24 %S A010999 1,47,1128,18424,230300,2349060,20358520,154143080,1040465790, %T A010999 6358402050,35607051480,184509266760,891794789340,4047376351620, %U A010999 17345898649800,70539987842520,273342452889765,1012974972473835,3601688791018080,12321566916640800,40661170824914640 %N A010999 a(n) = binomial coefficient C(n,46). %C A010999 Coordination sequence for 46-dimensional cyclotomic lattice Z[zeta_47]. %H A010999 T. D. Noe, Table of n, a(n) for n = 46..1000 %H A010999 Matthias Beck and Serkan Hosten, Cyclotomic polytopes and growth series of cyclotomic lattices, arXiv:math/0508136 [math.CO], 2005-2006. %H A010999 Index entries for linear recurrences with constant coefficients, 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 A010999 G.f.: x^46/(1-x)^47. - _Zerinvary Lajos_, Dec 20 2008 %F A010999 From _Amiram Eldar_, Dec 15 2020: (Start) %F A010999 Sum_{n>=46} 1/a(n) = 46/45. %F A010999 Sum_{n>=46} (-1)^n/a(n) = A001787(46)*log(2) - A242091(46)/45! = 1618481116086272*log(2) - 14357776821749670963095578951159/12798353476633725 = 0.9795596119... (End) %p A010999 seq(binomial(n,46),n=46..67); # _Zerinvary Lajos_, Dec 20 2008 %t A010999 Table[Binomial[n,46],{n,46,77}] (* _Vladimir Joseph Stephan Orlovsky_, May 16 2011 *) %o A010999 (Magma) [Binomial(n, 46): n in [46..70]]; // _Vincenzo Librandi_, Jun 12 2013 %Y A010999 Cf. A010997, A010998, A001787, A242091. %K A010999 nonn %O A010999 46,2 %A A010999 _N. J. A. Sloane_ # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE