Hello Wolfram killers,
Sasha was near, but how to obtain these two integrals? Ok 500 is to much for calculating, but 200, ok?
f[r_] := Sum[(((-1)^n*(2*r - 2*n - 7)!!)/(2^n*n!*(r - 2*n - 1)!))* x^(r - 2*n - 1), {n, 0, r/2}]; Nw := Transpose[Table[f[j], {i, 1}, {j, 5, 500, 1}]]; X1 = Integrate[Nw . Transpose[Nw], {x, -1, 1}]; Y1 = Integrate[D[Nw, {x, 2}] . Transpose[D[Nw, {x, 2}]], {x, -1, 1}]; MatrixForm[X1] MatrixForm[Y1]