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Nov 11, 2016 at 15:37 comment added Pietro Majer Your matrices $A_n$ may also be written in the form $D_nB_nD_n$, where $D_n:=\mathrm{diag}(1,1/2,1/3,1/4,..,1/n)$ and $B_n$ with entries $(\min\{i,j\})^2$. This $B_n^{-1}$ has a tridiagonal form like $M_n:=A_n^{-1}$, actually quite simpler.
Nov 11, 2016 at 11:31 history answered Pietro Majer CC BY-SA 3.0