x^n in Terms of the Derivatives of the Chebyshev Polynomials

1                              
0 1 0 0 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 0 0
0 2 0 1 0 0 0 0 0 0 0 0 0 0 0 0
2 0 3 0 1 0 0 0 0 0 0 0 0 0 0 0
0 5 0 4 0 1 0 0 0 0 0 0 0 0 0 0
5 0 9 0 5 0 1 0 0 0 0 0 0 0 0 0
0 14 0 14 0 6 0 1 0 0 0 0 0 0 0 0
14 0 28 0 20 0 7 0 1 0 0 0 0 0 0 0
0 42 0 48 0 27 0 8 0 1 0 0 0 0 0 0
42 0 90 0 75 0 35 0 9 0 1 0 0 0 0 0
0 132 0 165 0 110 0 44 0 10 0 1 0 0 0 0
132 0 297 0 275 0 154 0 54 0 11 0 1 0 0 0
0 429 0 572 0 429 0 208 0 65 0 12 0 1 0 0
429 0 1001 0 1001 0 637 0 273 0 77 0 13 0 1 0
0 1430 0 2002 0 1638 0 910 0 350 0 90 0 14 0 1
1430 0 3432 0 3640 0 2548 0 1260 0 440 0 104 0 15 0
0 4862 0 7072 0 6188 0 3808 0 1700 0 544 0 119 0 15
4862 0 11934 0 13260 0 9996 0 5508 0 2244 0 663 0 134 0
0 16796 0 25194 0 23256 0 15504 0 7752 0 2907 0 797 0 134
16796 0 41990 0 48450 0 38760 0 23256 0 10659 0 3704 0 931 0
0 58786 0 90440 0 87210 0 62016 0 33915 0 14363 0 4635 0 931
58786 0 149226 0 177650 0 149226 0 95931 0 48278 0 18998 0 5566 0



Reference: Abramowitz p.796.