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A156647 Square array T(n, k) = Product_{j=1..n} (1 - ChebyshevT(j, k+1)^2) with T(n, 0) = n!, read by antidiagonals.

%I A156647 #9 Sep 08 2022 08:45:41
%S A156647 1,1,1,1,-3,2,1,-8,144,6,1,-15,2304,-97200,24,1,-24,14400,-22579200,
%T A156647 914457600,120,1,-35,57600,-857304000,7517247897600,-119833267276800,
%U A156647 720,1,-48,176400,-13548902400,3163657512960000,-85018329720343756800,218719679433615360000,5040
%N A156647 Square array T(n, k) = Product_{j=1..n} (1 - ChebyshevT(j, k+1)^2) with T(n, 0) = n!, read by antidiagonals.
%H A156647 G. C. Greubel, <a href="/A156647/b156647.txt">Antidiagonal rows n = 0..25, flattened</a>
%F A156647 T(n, k) = Product_{j=1..n} (1 - ChebyshevT(j, k+1)^2) with T(n, 0) = n! (square array).
%e A156647 Square array begins as:
%e A156647     1,                1,                     1, ...;
%e A156647     1,               -3,                    -8, ...;
%e A156647     2,              144,                  2304, ...;
%e A156647     6,           -97200,             -22579200, ...;
%e A156647    24,        914457600,         7517247897600, ...;
%e A156647   120, -119833267276800, -85018329720343756800, ...;
%e A156647 Triangle begins as:
%e A156647   1;
%e A156647   1,   1;
%e A156647   1,  -3,     2;
%e A156647   1,  -8,   144,          6;
%e A156647   1, -15,  2304,     -97200,            24;
%e A156647   1, -24, 14400,  -22579200,     914457600,              120;
%e A156647   1, -35, 57600, -857304000, 7517247897600, -119833267276800, 720;
%t A156647 T[n_, k_]= If[k==0, n!, Product[1 - ChebyshevT[j, k+1]^2, {j,n}]];
%t A156647 Table[T[k, n-k], {n,0,12}, {k,0,n}]//Flatten (* modified by _G. C. Greubel_, Jul 02 2021 *)
%o A156647 (Magma)
%o A156647 T:= func< n,k | n eq 0 select 1 else k eq 0 select Factorial(n) else (&*[1 - Evaluate(ChebyshevT(j), k+1)^2 : j in [1..n]]) >;
%o A156647 [T(k, n-k): k in [0..n], n in [0..12]]; // _G. C. Greubel_, Jul 02 2021
%o A156647 (Sage)
%o A156647 def T(n,k): return factorial(n) if (k==0) else product( 1 - chebyshev_T(j, k+1)^2 for j in (1..n) )
%o A156647 flatten([[T(k, n-k) for k in (0..n)] for n in (0..12)]) # _G. C. Greubel_, Jul 02 2021
%Y A156647 Cf. A123583.
%K A156647 sign,tabl
%O A156647 0,5
%A A156647 _Roger L. Bagula_, Feb 12 2009
%E A156647 Edited by _G. C. Greubel_, Jul 02 2021