Let \({\mathfrak g}\) be the Lie algebra of all upper triangular matrices over a finite field \(F_ q\). A combinatorial interpretation of the number \(O_{n,q}\) of all orbits of \({\mathfrak g}\) in \({\mathfrak g}^*\) is given as some partition function. It is proved that \(O_{n,q}\) is proportional to the number of all pairs of commuting elements in \({\mathfrak g}\). A connection of \(O_{n,q}\) for \(q=2\) to Euler-Bernoulli numbers \(K_{n+1}\) is discussed. The inequality \(O_{n,q}\geq K_{n+1}\) is conjectured.