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A357892 T(n,k) are the values of a variant of the Chebyshev polynomials P(n,x) of order n evaluated at x = k, where T(n,k), n >= 0, k <= n is a triangle read by rows. P(0,x) = 1, P(1,x) = x, P(n,x) = x*P(n-1,x) - P(n-2,x).

%I A357892 #6 Oct 19 2022 06:49:13
%S A357892 1,0,1,-1,0,3,0,-1,4,21,1,-1,5,55,209,0,0,6,144,780,2640,-1,1,7,377,
%T A357892 2911,12649,40391,0,1,8,987,10864,60605,235416,726103,1,0,9,2584,
%U A357892 40545,290376,1372105,4976784,15003009,0,-1,10,6765,151316,1391275,7997214,34111385,118118440,350382231
%N A357892 T(n,k) are the values of a variant of the Chebyshev polynomials P(n,x) of order n evaluated at x = k, where T(n,k), n >= 0, k <= n is a triangle read by rows. P(0,x) = 1, P(1,x) = x, P(n,x) = x*P(n-1,x) - P(n-2,x).
%e A357892 The triangle begins:
%e A357892    1;
%e A357892    0,  1;
%e A357892   -1,  0, 3;
%e A357892    0, -1, 4,  21;
%e A357892    1, -1, 5,  55,   209;
%e A357892    0,  0, 6, 144,   780,  2640;
%e A357892   -1,  1, 7, 377,  2911, 12649,  40391;
%e A357892    0,  1, 8, 987, 10864, 60605, 235416, 726103
%o A357892 (PARI) chp(k,x) = if(k==0, 1, if(k==1, x, x*chp(k-1,x) - chp(k-2,x)));
%o A357892 for (k=0, 9, for(x=0, k, print1(ch(k,x),", ")); print())
%Y A357892 Cf. A001353 (column 4), A001906 (column 3), A097690 (diagonal).
%K A357892 sign,tabl
%O A357892 0,6
%A A357892 _Hugo Pfoertner_, Oct 18 2022