a(n,m) tabl head (triangle) for A127677 Coefficient table of scaled Chebyshev 2*T(2*n,x) polynomials, increasing even scaled powers, without zeros. n\m 0 1 2 3 4 5 6 7 8 9 ... 0 2 0 0 0 0 0 0 0 0 0 1 -2 1 0 0 0 0 0 0 0 0 2 2 -4 1 0 0 0 0 0 0 0 3 -2 9 -6 1 0 0 0 0 0 0 4 2 -16 20 -8 1 0 0 0 0 0 5 -2 25 -50 35 -10 1 0 0 0 0 6 2 -36 105 -112 54 -12 1 0 0 0 7 -2 49 -196 294 -210 77 -14 1 0 0 8 2 -64 336 -672 660 -352 104 -16 1 0 9 -2 81 -540 1386 -1782 1287 -546 135 -18 1 . . . 2*T(2*n,x) = sum(a(n,m)*(2*x)^(2*m),m=0..n). Row sums (signed): -A061347(n+3),n>=0: periodic [2,-1,-1] sequence with period 3. Row sums (unsigned): A005248(n)=L(2*n) (Lucas numbers with even index). ######################### e.o.f. ####################################################