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A014064 Coefficients of the reciprocal of the 55th cyclotomic polynomial.

%I A014064 #30 Jan 27 2019 09:51:42
%S A014064 1,1,1,1,1,0,0,0,0,0,0,-1,-1,-1,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
%T A014064 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0,0,
%U A014064 -1,-1,-1,-1,-1,0,0,0,0,0,0,0,0,0,0
%N A014064 Coefficients of the reciprocal of the 55th cyclotomic polynomial.
%C A014064 Periodic with period length 55. - _Ray Chandler_, Apr 03 2017
%H A014064 Vincenzo Librandi, <a href="/A014064/b014064.txt">Table of n, a(n) for n = 0..1000</a>
%H A014064 <a href="/index/Rec#order_40">Index entries for linear recurrences with constant coefficients</a>, signature (1, 0, 0, 0, -1, 1, 0, 0, 0, -1, 0, 1, 0, 0, -1, 0, 1, 0, 0, -1, 0, 0, 1, 0, -1, 0, 0, 1, 0, -1, 0, 0, 0, 1, -1, 0, 0, 0, 1, -1).
%H A014064 <a href="/index/Pol#poly_cyclo_inv">Index to sequences related to inverse of cyclotomic polynomials</a>
%F A014064 a(n) = (5*w - 1)*(w - 2)*(w - 3)*(w - 4)*(63*m^4 - 350*m^3 + 630*m^2 - 325*m + 12)*(m - 5)!/(43545600*(m - 11)!), where m = n mod 11 and w = floor(n/11) mod 5. - _Luce ETIENNE_, Nov 21 2018
%p A014064 with(numtheory,cyclotomic); c := n->series(1/cyclotomic(n,x),x,80);
%t A014064 CoefficientList[Series[1/Cyclotomic[55, x], {x, 0, 200}], x] (* _Vincenzo Librandi_, Apr 05 2014 *)
%t A014064 LinearRecurrence[{1, 0, 0, 0, -1, 1, 0, 0, 0, -1, 0, 1, 0, 0, -1, 0, 1, 0, 0, -1, 0, 0, 1, 0, -1, 0, 0, 1, 0, -1, 0, 0, 0, 1, -1, 0, 0, 0, 1, -1},{1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},81] (* _Ray Chandler_, Sep 15 2015 *)
%o A014064 (PARI) Vec(1/polcyclo(55) + O(x^99)) \\ _Michel Marcus_, Jan 25 2019
%Y A014064 Cf. similar sequences listed in A240328.
%Y A014064 Cf. A010880, A010874.
%K A014064 sign,easy
%O A014064 0,1
%A A014064 _Simon Plouffe_
%E A014064 Name edited by _Wolfdieter Lang_, Jan 25 2019