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By studying Cameron's operator in terms of determinants, two kinds of"integer" sequences of incomplete numbers were introduced. One was the sequenceof restricted numbers, including $s$-step Fibonacci sequences. Another was thesequence of associated numbers, including Lam\'e sequences of higher order. Bythe classical Trudi's formula and the inverse relation, more expressions wereable to be obtained. These relations and identities can be extended to those ofsequence of negative integers or rational numbers. As applications, we considerhypergeometric Bernoulli, Cauchy and Euler numbers with some modifications.

Cameron's operator in terms of determinants, and hypergeometric numbers