There are many rectangular arrays whose \(n^{th}\) column is the \(n\)-fold convolution of the \(0^{th}\) column in combinatorics. For this type of rectangular arrays, we prove a formula for evaluating the determinant of certain submatrices, which was conjectured by Hoggatt and Bicknell. Our result unifies the determinant evaluation of submatrices of the rectangular arrays consisting of binomial coefficients, multinomial coefficients, Fibonacci numbers, Catalan numbers, generalized Catalan and Motzkin numbers.
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