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A179838 Triangle T(n,k) read by rows: the coefficient [x^k] of the product_{s=1..n} (x+64*cos(s*Pi/(2n+1))^6), 0<=k<=n.

%I A179838 #25 Apr 13 2021 18:53:56
%S A179838 1,1,1,1,18,1,1,129,38,1,1,571,627,58,1,1,1884,6212,1525,78,1,1,5103,
%T A179838 43123,24576,2823,98,1,1,11998,230241,277500,63660,4521,118,1,1,25362,
%U A179838 1005267,2379096,1014681,131464,6619,138,1,1,49347,3744753,16359996,12301986,2724266,235988,9117,158,1
%N A179838 Triangle T(n,k) read by rows: the coefficient [x^k] of the product_{s=1..n} (x+64*cos(s*Pi/(2n+1))^6), 0<=k<=n.
%C A179838 Polynomial coefficients of H_n^(3)(x) by Bostan et al.
%H A179838 Andrew Howroyd, <a href="/A179838/b179838.txt">Table of n, a(n) for n = 0..1325</a> (rows 0..50)
%H A179838 Alin Bostan, Bruno Salvy, Khang Tran, <a href="https://hal.inria.fr/inria-00400839">Generating functions of Chebyshev-like polynomials</a>, 2009.
%H A179838 Alin Bostan, Bruno Salvy, et al., <a href="http://dx.doi.org/10.1142/S1793042110003691">Generating functions of Chebyshev-like polynomials</a>, Intl. J. Number Theory 6 (7) (2010) 1659
%F A179838 A(x;t) = Sum_{n>=0} P_n(t)*x^n = (1-x)*((x-1)^6 - t*x^2*(x+3)*(3*x+1))/(t^2*x^4-t*x*(x^4+14*x^3+34*x^2+14*x+1)*(x-1)^2+(x-1)^8), where P_n(t) = Sum_{k=0..n} T(n,k)*t^k. - _Gheorghe Coserea_, Apr 20 2017
%e A179838 1
%e A179838 1 1
%e A179838 1 18 1
%e A179838 1 129 38 1
%e A179838 1 571 627 58 1
%e A179838 1 1884 6212 1525 78 1
%e A179838 1 5103 43123 24576 2823 98 1
%e A179838 1 11998 230241 277500 63660 4521 118 1
%e A179838 1 25362 1005267 2379096 1014681 131464 6619 138 1
%e A179838 1 49347 3744753 16359996 12301986 2724266 235988 9117 158 1
%o A179838 (PARI)
%o A179838 my(x='x+O('x^10)); concat(apply(p->Vecrev(p), Vec(Ser((1-x)*((x-1)^6 - t*x^2*(x+3)*(3*x+1))/(t^2*x^4-t*x*(x^4+14*x^3+34*x^2+14*x+1)*(x-1)^2+(x-1)^8))))) \\ _Gheorghe Coserea_, Apr 20 2017
%Y A179838 Column k=1 is A244879.
%Y A179838 Cf. A179837.
%K A179838 tabl,nonn
%O A179838 0,5
%A A179838 _R. J. Mathar_, Jan 10 2011
%E A179838 Terms a(38) and beyond from _Andrew Howroyd_, Apr 13 2021