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
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
Crossrefs
Programs
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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.