  Gessel's famous Bessel determinant formula gives the generating function of
the number of permutations without increasing subsequences of a given length.
Ekhad and Zeilberger proposed the challenge of finding a suitable
generalization for permutations of multisets in which all multiplicities are
equal, that is, to count words of length $rn$ from an alphabet consisting of
$n$ letters in which each letter appears exactly $r$ times and which have no
increasing subsequences of length $d$.
  In this paper we present such a generating function expressible as a multiple
integral of the product of a Gessel-type Toeplitz determinant with the
exponentiated cycle index polynomial of the symmetric group on $r$ elements.
