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%I #6 Sep 08 2022 08:45:33
%S -64,640,-3456,13440,-42240,114048,-274560,604032,-1235520,2379520,
%T -4356352,7637760,-12899328,21085440,-33488640,51845376,-78450240,
%U 116290944,-169206400,242070400,-341003520,473616000,-649284480,879465600,-1178049600
%N C(n+7, 7)*(n+4)*(-1)^(n+1)*16.
%C Fifth column of the triangle defined in A123588, ninth column of the triangle defined in A123583.
%H <a href="/index/Ch#Cheby">Index entries for sequences related to Chebyshev polynomials.</a>
%F a(n) = coefficient of x^8 in the polynomial 1 - T_(n+4)(x)^2, where T_n(x) is the n-th Chebyshev polynomial of the first kind.
%F G.f.: 64*(x-1)/(x+1)^9.
%F a(n) = (-1)^(n+1)*64*A053347(n).
%o (Magma) [ Binomial(n+7, 7)*(n+4)*(-1)^(n+1)*16: n in [0..24] ];
%o (Magma) k:=4; [ Coefficients(1-ChebyshevT(n+k)^2)[2*k+1]: n in [0..24] ];
%o (PARI) for(n=0,24,print1(polcoeff(taylor(64*(x-1)/(x+1)^9,x),n),","));
%Y Cf. A007318 (Pascal's triangle), A123588, A123583, A053347.
%K sign
%O 0,1
%A _Klaus Brockhaus_, Mar 15 2008
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