Cameron’s operator in terms of determinants and hypergeometric numbers

By studying Cameron’s operator in terms of determinants, two kinds “integer” sequences incomplete numbers were introduced. One was the sequence restricted numbers, including s-step Fibonacci sequences. Another associated Lamé higher order. classical Trudi’s formula and inverse relation, more expressions able to be obtained. These relations identities can extended those negative integers or rational numbers. As applications, we consider hypergeometric Bernoulli, Cauchy Euler with some modifications.