I need matrix H. G is working, but H is just derivative?? How to obtain?
g = Integrate[x^(p + q - 2*(m + n + 1)), {x, -1, 1}]; h = Integrate[D[x^(p + q - 2*(m + n + 1)), {x, 2}], {x, -1, 1}]; c[r_, n_] := ((-1)^n (2 r - 2 n - 7)!!)/(2^n n! (r - 2 n - 1)!); G = Table[Sum[c[p, n] c[q, m] (g), {m, 0, (q - 1)/2}, {n, 0, (p - 1)/2}], {p, 5, 12}, {q, 5, 12}]; H = Table[Sum[c[p, n] c[q, m] (h), {m, 0, (q - 1)/2}, {n, 0, (p - 1)/2}], {p, 5, 12}, {q, 5, 12}]; G // MatrixForm H // MatrixForm