Matricial formulae for partitions
  The exponential of the triangular matrix whose entries in the diagonal at distance $n$ from the principal diagonal are all equal to the sum of the inverse of the divisors of $n$ is the triangular matrix whose entries in the diagonal at distance $n$ from the principal diagonal are all equal to the number of partitions of $n$. A similar result is true for any pair of sequences satisfying a special recurrence. 
Aicardi Francesca