andydude Wrote:

Hmm, nice coincidence here. Did you notice, that the fractional entries are just the bernoulli-numbers, resp binomially weighted bernoulli-numbers? It would be more obvious, if your matrix were of bigger size (but I don't know, which iterative function that required). When I was fiddling with the pascal-matrix last year I found the inverse of the shifted pascal-matrix (where -before shifting- the diagonal is removed) is just a matrix containing the bernoulli-numbers as it was found by Faulhaber and J Bernoulli, giving coefficients (with a little modification) of bernoulli-polynomials. I found, that it is part of the eigensystem for the *column-signed* pascal-matrix. Perhaps you like to have a look at my according small treatise at p-matrix

Things converge...

Gottfried

Gottfried Helms, Kassel