On the determinants of the square-type Stirling matrix and Bell matrix (Q2119860)

Summary: We study determinants of the square-type Stirling matrix \(S^\ast\) and the square-type Bell matrix \(B^\ast\). For this purpose, we prove that \(S^\ast\) and \(B^\ast\) have LU factorizations \(S^\ast= L_S U_S\) and \(B^\ast= L_B U_B\) where the diagonal entries of \(U_S\) are \(k^{k - 1}\), while those of \(U_B\) are \(k! (k\geq1)\).