Coefficients of x^n in terms of Chebyshev Polynomials U_n 

http://www.math.nthu.edu.tw/123/test/xn-un.123


1                      
0 1 0 0 0 0 0 0 0 0 0 0
1 0 1 0 0 0 0 0 0 0 0 0
0 2 0 1 0 0 0 0 0 0 0 0
2 0 3 0 1 0 0 0 0 0 0 0
0 5 0 4 0 1 0 0 0 0 0 0
5 0 9 0 5 0 1 0 0 0 0 0
0 14 0 14 0 6 0 1 0 0 0 0
14 0 28 0 20 0 7 0 1 0 0 0
0 42 0 48 0 27 0 8 0 1 0 0
42 0 90 0 75 0 35 0 9 0 1 0
0 132 0 165 0 110 0 44 0 10 0 1

 Reference: Abramowitz p. 796.