a(n,m) tabl head (triangle) for  A127674

 Chebyshev T-polynomials T(2*n,x) coefficients, increasing even powers of x.


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

   0       1       0        0         0         0          0         0          0        0

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

   2       1      -8        8         0         0          0         0          0        0      0         0

   3      -1      18      -48        32         0          0         0          0        0      0         0

   4       1     -32      160      -256       128          0         0          0        0      0         0

   5      -1      50     -400      1120     -1280        512         0          0        0      0         0

   6       1     -72      840     -3584      6912      -6144      2048          0        0      0         0

   7      -1      98    -1568      9408    -26880      39424    -28672       8192        0      0         0

   8       1    -128     2688    -21504     84480    -180224    212992    -131072    32768      0         0

   9      -1     162    -4320     44352   -228096     658944  -1118208    1105920  -589824   131072       0

  10       1    -200     6600    -84480    549120   -2050048   4659200   -6553600  5570560 -2621440  524288
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 The rows for n=11..15 are:

 n=11:  [-1, 242, -9680, 151008, -1208064, 5637632, -16400384, 30638080, -36765696, 27394048, -11534336, 2097152]

 n=12:  [1, -288, 13728, -256256, 2471040, -14057472, 50692096, -120324096, 190513152, -199229440, 132120576, -50331648, 8388608] 

 n=13:  [-1, 338, -18928, 416416, -4759040, 32361472, -141213696, 412778496, -825556992, 1133117440, -1049624576, 627048448, -218103808, 33554432]
 
 n=14:  [1, -392, 25480, -652288, 8712704, -69701632, 361181184, -1270087680, 3111714816, -5369233408, 6499598336, -5402263552, 2936012800, -939524096, 134217728]


 n=15:  [-1, 450, -33600, 990080, -15275520, 141892608, -859955200, 3572121600, -10478223360, 22052208640, -33426505728, 36175872000, -27262976000, 13589544960, -4026531840, 536870912] 


 Chebyshev's T(2*n,x) polynomials are:

  n=0: 1
  n=1: -1+2*x^2
  n=2: 1-8*x^2+8*x^4
  n=3: -1+18*x^2-48*x^4+32*x^6
  n=4: 1-32*x^2+160*x^4-256*x^6+128*x^8
  n=5: -1+50*x^2-400*x^4+1120*x^6-1280*x^8+512*x^10
  n=6: 1-72*x^2+840*x^4-3584*x^6+6912*x^8-6144*x^10+2048*x^12
  n=7: -1+98*x^2-1568*x^4+9408*x^6-26880*x^8+39424*x^10-28672*x^12+8192*x^14
  n=8: 1-128*x^2+2688*x^4-21504*x^6+84480*x^8-180224*x^10+212992*x^12-131072*x^14+32768*x^16
  n=9: -1+162*x^2-4320*x^4+44352*x^6-228096*x^8+658944*x^10-1118208*x^12+1105920*x^14-589824*x^16+131072*x^18
 n=10: 1-200*x^2+6600*x^4-84480*x^6+549120*x^8-2050048*x^10+4659200*x^12-6553600*x^14+5570560*x^16-2621440*x^1+       +524288*x^2


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