  Let K be a (commutative) field and consider a nonzero element q in K which is
not a root of unity. Goodearl and Lenagan have shown that the number of
H-primes in the algebra R of m times p quantum matrices which contain all (t+1)
times (t+1) quantum minors but not all t times t quantum minors is a perfect
square. The aim of this paper is to make precise their result: we prove that
this number is equal to (t!)^2 S(n+1,t+1)^2, where S(n+1,t+1) denotes the
Stirling number of second kind associated to n+1 and t+1. This result was
conjectured by Goodearl, Lenagan and McCammond. The proof involves some closed
formulas for the poly-Bernoulli numbers that were established by Arakawa-Kaneko
and Kaneko.
