A101124 Number triangle associated to Chebyshev polynomials of first kind.

1, 0, 1, -1, 1, 1, 0, 1, 2, 1, 1, 1, 7, 3, 1, 0, 1, 26, 17, 4, 1, -1, 1, 97, 99, 31, 5, 1, 0, 1, 362, 577, 244, 49, 6, 1, 1, 1, 1351, 3363, 1921, 485, 71, 7, 1, 0, 1, 5042, 19601, 15124, 4801, 846, 97, 8, 1, -1, 1, 18817, 114243, 119071, 47525, 10081, 1351, 127, 9, 1, 0, 1, 70226, 665857, 937444, 470449, 120126, 18817, 2024, 161

Offset: 0

Author

Paul Barry, Dec 02 2004

Keywords

• easy
• sign
• tabl

Examples

			As a number triangle, rows begin:
  {1},
  {0,1},
  {-1,1,1},
  {0,1,2,1},
  ...
As a square array, rows begin
   1, 1,  1,   1,    1, ...
   0, 1,  2,   3,    4, ...
  -1, 1,  7,  17,   31, ...
   0, 1, 26,  99,  244, ...
   1, 1, 97, 577, 1921, ...
		

Links

• Seiichi Manyama, Antidiagonals n = 0..139, flattened
• Index entries for sequences related to Chebyshev polynomials.

Crossrefs

Columns include A001075, A001541, A001091, A001079, A023038, A011943.

Row sums are A101125.

Diagonal sums are A101126.

Main diagonal gives A115066.

Mirror of A322836.

Cf. A053120.

Programs

Mathematica

T[n_, k_] := SeriesCoefficient[x^k (1 - k x)/(1 - 2 k x + x^2), {x, 0, n}];
Table[T[n, k], {n, 0, 11}, {k, 0, n}] // Flatten (* Jean-François Alcover, Jun 12 2017 *)

Formula

Number triangle S(n, k)=T(n-k, k), k

Columns have g.f. x^k(1-kx)/(1-2kx+x^2).

Also, square array if(n=0, 1, T(n, k)) read by antidiagonals.

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