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%I #20 Apr 21 2017 12:32:47
%S 1,1,1,1,7,1,1,26,13,1,1,70,87,19,1,1,155,403,184,25,1,1,301,1462,
%T 1216,317,31,1,1,532,4446,6190,2725,486,37,1,1,876,11826,25954,17903,
%U 5146,691,43,1,1,1365,28314,93536,96055,41461,8695,932,49,1,1,2035
%N Triangle T(n,k) read by rows: the coefficient [x^k] of the product_{s=1..n} (x+16*cos(s*Pi/(2n+1))^4), 0<=k<=n.
%C Polynomial coefficients of H_n^(2)(x) by Bostan et al.
%H Alin Bostan, Bruno Salvy, Khang Tran, <a href="https://hal.inria.fr/inria-00400839">Generating functions of Chebyshev-like polynomials</a>, 2009.
%H 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 T(n,1) = A006325(n+1).
%F A(x;t) = Sum_{n>=0} P_n(t)*x^n = (1-x)^3/((x-1)^4 - t*x*(x+1)^2), where P_n(t) = Sum_{k=0..n} T(n,k)*t^k. - _Gheorghe Coserea_, Apr 20 2017
%e 1
%e 1 1
%e 1 7 1
%e 1 26 13 1
%e 1 70 87 19 1
%e 1 155 403 184 25 1
%e 1 301 1462 1216 317 31 1
%e 1 532 4446 6190 2725 486 37 1
%e 1 876 11826 25954 17903 5146 691 43 1
%e 1 1365 28314 93536 96055 41461 8695 932 49 1
%e 1 2035 62271 298376 439019 271467 83020 13588 1209 55 1
%o (PARI)
%o x='x+O('x^11); concat(apply(p->Vecrev(p), Vec(Ser((1-x)^3/((x-1)^4 - t*x*(x+1)^2))))) \\ _Gheorghe Coserea_, Apr 20 2017
%Y Cf. A179838
%K tabl,nonn
%O 0,5
%A _R. J. Mathar_, Jan 10 2011
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