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C(n+9, 9)*(n+5)*(-1)^(n+1)*256/5.
0

%I #6 Sep 08 2022 08:45:33

%S -256,3072,-19712,90112,-329472,1025024,-2818816,7028736,-16180736,

%T 34850816,-70946304,137592832,-255836672,458422272,-794962432,

%U 1338884096,-2196606720,3519493120,-5519205120,8487198720,-12819206400,19045678080,-27869287680

%N C(n+9, 9)*(n+5)*(-1)^(n+1)*256/5.

%C Sixth column of the triangle defined in A123588, eleventh 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^10 in the polynomial 1 - T_(n+5)(x)^2, where T_n(x) is the n-th Chebyshev polynomial of the first kind.

%F G.f.: 256*(x-1)/(x+1)^11.

%F a(n) = (-1)^(n+1)*256*A054334(n).

%o (Magma) [ Binomial(n+9, 9)*(n+5)*(-1)^(n+1)*256/5: n in [0..22] ];

%o (Magma) k:=5; [ Coefficients(1-ChebyshevT(n+k)^2)[2*k+1]: n in [0..22] ];

%o (PARI) for(n=0,22,print1(polcoeff(taylor(256*(x-1)/(x+1)^11,x),n),","));

%Y Cf. A007318 (Pascal's triangle), A123588, A123583, A054334.

%K sign

%O 0,1

%A _Klaus Brockhaus_, Mar 15 2008