(*Norm of Eigenvectors from Eigenvalues*)
(*start*)
Clear[nn, t, n, k, M, x];
nn = 11;
t[n_, 1] = 1;
t[1, k_] = 1;
t[n_, k_] :=
t[n, k] =
If[n < k,
If[And[n > 1, k > 1], -Sum[t[k - i, n], {i, 1, n - 1}], 0],
If[And[n > 1, k > 1], -Sum[t[n - i, k], {i, 1, k - 1}], 0]];

T = Table[Table[t[n, k], {k, 1, nn}], {n, 1, nn}];
HermitianMatrixQ[T]

TableForm[A = Table[Table[T[[n, k]], {k, 1, nn}], {n, 1, nn}]];
lambdaA = N[Eigenvalues[A]];
TableForm[M = Table[Table[T[[n, k]], {k, 1, nn - 1}], {n, 1, nn - 1}]];