  We exhibit a lower-triangular matrix of polynomials $T(a,c,d,e,f,g)$ in six
indeterminates that appears empirically to be coefficientwise totally positive,
and which includes as a special case the Eulerian triangle. We prove the
coefficientwise total positivity of $T(a,c,0,e,0,0)$, which includes the
reversed Stirling subset triangle.
