a(n,m) tabl head (triangle) for  A128497
 
 Coefficient table for sum(S(k,x)*S(k+1,x)/x,k=0..n) (Chebyshev's S-polynomials)


   n\m    0      1       2       3        4       5       6      7      8    9   10 ...

   0      1      0       0       0        0       0       0      0      0    0    0
   1      0      1       0       0        0       0       0      0      0    0    0
   2      2     -2       1       0        0       0       0      0      0    0    0
   3      0      5      -4       1        0       0       0      0      0    0    0
   4      3     -8      12      -6        1       0       0      0      0    0    0
   5      0     14     -28      23       -8       1       0      0      0    0    0
   6      4    -20      58     -68       38     -10       1      0      0    0    0
   7      0     30    -108     171     -136      57     -12      1      0    0    0
   8      5    -40     188    -382      405    -240      80    -14      1    0    0
   9      0     55    -308     781    -1056     828    -388    107    -16    1    0
  10      6    -70     483   -1488     2488   -2472    1524   -588    138  -18    1
   .
   .
   .

 The rows n=11..15 are:

 n=11: [0, 91, -728, 2678, -5408, 6604, -5132, 2593, -848, 173, -20, 1]
 n=12: [7, -112, 1064, -4596, 11006, -16144, 15344, -9730, 4151, -1176, 212, -22, 1]
 n=13: [0, 140, -1512, 7578, -21200, 36690, -41700, 32211, -17184, 6330, -1580, 255, -24, 1]
 n=14: [8, -168, 2100, -12072, 38972, -78436, 104746, -96392, 62428, -28668, 9278, -2068, 302, -26, 1]
 n=15: [0, 204, -2856, 18666, -68816, 159154, -246228, 265319, -204064, 113434, -45644, 13159, -2648, 
       353, -28, 1]

  
 Row sums (signed) look like A008620: [1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, ...]
 with g.f. 1/((1-x)*(1-x^3).

 Row sums (unsigned) look like |A077916|. [1, 1, 5, 10, 30, 74, 199, 515, 1355, 3540, 9276, 24276, 63565, 166405, 435665, 1140574,...]
  with g.f. 1/((1+x)*(1-2*x-2*x^2-x^3)).


 The g.f.s for the column sequences (without leading zeros) are:

 1/(((1-x)^2)*(1+x)^(2*m)).
 
 Therefore, this is a Riordan lower triangular matrix (1/(1-x)^2, x/(1+x)^2).


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