looks pretty much as the classical Hilbert matrix

In [2] it was noticed that the reciprocal Fibonacci numbers form a moment sequence of a positive discrete measure, and the corresponding orthogonal polynonials were identified as special little q-Jacobi polyno-mials corresponding to the value q = (1−√5)/(1 +√5). The Hankel matrix of reciprocal Fibonacci numbers, called the Fil-bert matrix in [3]