a(n,m) tabl head (triangle) for  A053120 
 
 Coefficients for Chebyshev T-polynomials


   n\m     0     1      2       3      4       5       6       7      8      9     10     11    12

   0       1     0      0       0      0       0       0       0      0      0      0      0     0

   1       0     1      0       0      0       0       0       0      0      0      0      0     0

   2      -1     0      2       0      0       0       0       0      0      0      0      0     0

   3       0    -3      0       4      0       0       0       0      0      0      0      0     0

   4       1     0     -8       0      8       0       0       0      0      0      0      0     0

   5       0     5      0     -20      0      16       0       0      0      0      0      0     0   

   6      -1     0     18       0    -48       0      32       0      0      0      0      0     0

   7       0    -7      0      56      0    -112       0      64      0      0      0      0     0

   8       1     0    -32       0    160       0    -256       0    128      0      0      0     0

   9       0     9      0    -120      0     432       0    -576      0    256      0      0     0

  10      -1     0     50       0   -400       0    1120       0  -1280      0    512      0     0

  11       0   -11      0     220      0   -1232       0    2816      0  -2816      0   1024     0

  12       1     0    -72       0    840       0   -3584       0   6912      0  -6144      0  2048


 This confirms the Abramowitz-Stegun table p.795.

 The rows n=13 to 20 are:

 n=13: [0, 13, 0, -364, 0, 2912, 0, -9984, 0, 16640, 0, -13312, 0, 4096]

 n=14: [-1, 0, 98, 0, -1568, 0, 9408, 0, -26880, 0, 39424, 0, -28672, 0, 8192]

 n=15: [0, -15, 0, 560, 0, -6048, 0, 28800, 0, -70400, 0, 92160, 0, -61440, 0, 16384]

 n=16: [1, 0, -128, 0, 2688, 0, -21504, 0, 84480, 0, -180224, 0, 212992, 0, -131072, 0, 32768]
 
 n=17: [0, 17, 0, -816, 0, 11424, 0, -71808, 0, 239360, 0, -452608, 0, 487424, 0, -278528, 0, 65536]
 
 n=18: [-1, 0, 162, 0, -4320, 0, 44352, 0, -228096, 0, 658944, 0, -1118208, 0, 1105920, 0, -589824, 0, 131072]
 n=19: [0, -19, 0, 1140, 0, -20064, 0, 160512, 0, -695552, 0, 1770496, 0, -2723840, 0, 2490368, 0, -1245184, 0, 262144]
 
 n=20: [1, 0, -200, 0, 6600, 0, -84480, 0, 549120, 0, -2050048, 0, 4659200, 0, -6553600, 0, 5570560, 0, -2621440, 0, 524288][1, 0, -200, 0, 6600, 0, -84480, 0, 549120, 0, -2050048, 0, 4659200, 0, -6553600, 0, 5570560, 0, -2621440, 0, 524288]



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