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).

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, 2911, 12649, 40391, 0, 1, 8, 987, 10864, 60605, 235416, 726103, 1, 0, 9, 2584, 40545, 290376, 1372105, 4976784, 15003009, 0, -1, 10, 6765, 151316, 1391275, 7997214, 34111385, 118118440, 350382231

Offset

0,6

Links

Table of n, a(n) for n=0..54.

Example

The triangle begins:
   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,  2911, 12649,  40391;
   0,  1, 8, 987, 10864, 60605, 235416, 726103

Prog

(PARI) chp(k, x) = if(k==0, 1, if(k==1, x, x*chp(k-1, x) - chp(k-2, x)));
for (k=0, 9, for(x=0, k, print1(ch(k, x), ", ")); print())

Crossrefs

Cf. A001353 (column 4), A001906 (column 3), A097690 (diagonal).

Sequence in context: A079520 A229001 A208981 * A261158 A207543 A191532

Adjacent sequences: A357889 A357890 A357891 * A357893 A357894 A357895

Keyword

sign,tabl

Author

Hugo Pfoertner, Oct 18 2022

Status

approved