On the Determinants of the Square-Type Stirling Matrix and Bell Matrix

We study determinants of the square-type Stirling matrix S ∗ and the square-type Bell matrix B ∗ . For this purpose, we prove that S ∗ and B ∗ have LU factorizations S ∗ = L S U S and B ∗ = L B U B where the diagonal entries of U S are k k − 1 , while those of U B are k ! ( k ≥ 1 ).