%I
%S 1,1,1,2,1,1,2,3,3,1,3,3,8,5,1,3,6,16,17,7,1,4,6,30,45,30,9,
%T 1,4,10,50,103,98,47,11,1,5,10,80,211,269,183,68,13,1,5,15,
%U 120,399,651,588,308,93,15,1,6,15,175,707,1432,1644,1136,481,122,17,1,6,21,245,1190,2920,4132,3608
%N Coefficient table for sums of squares of Chebyshev's SPolynomials.
%C See A049310 for the coefficient table of Chebyshev's S(n,x)=U(n,x/2) polynomials.
%C The triangle for the coefficients of x^2 in S(n,x)^2 is A158454.  _Wolfdieter Lang_, Oct 18 2012
%H W. Lang, <a href="/A128495/a128495.txt">First 15 rows.</a>
%F S(2;n,x):=sum(S(k,x)^2,k=0..n)=sum(a(n,m)*x^(2*m),m=0..n), n>=0.
%F a(n,m)=[x^m](n+2T(n+1,x/2)*U(n+1,x/2))/(2*(1(x/2)^2)).
%e [1]; [1,1]; [2,1,1]; [2,3,3,1]; [3,3,8,5,1]; [3,6,16,17,7,1]; ...
%e Row polynomial S(2;4,x)=33*x^2+8*x^45*x^6+x^8 = sum(S(k,x)^2,k=0..4).
%e (4+2T(4+1,x/2)*U(4+1,x/2))/(2*(1(x/2)^2))= S(2;4,x)
%Y Row sums (signed) look like: A004523. Row sums (unsigned): A128496.
%Y Cf. A128494 =S(1; n, m).
%K sign,easy,tabl
%O 0,4
%A _Wolfdieter Lang_ Apr 04 2007
