Abstract
In the paper, the authors establish closed forms for the Delannoy two-functional sequence and its difference in terms of the Hessenberg determinants, derive recursive relations for the Delannoy two-functional sequence and its difference, and deduce closed forms, in terms of the Hessenberg determinants, and recursive relations for the Delannoy one-functional sequence, the Delannoy numbers, and central Delannoy numbers. In the paper, the authors establish closed forms for the Delannoy two-functional sequence and its difference in terms of the Hessenberg determinants, derive recursive relations for the Delannoy two-functional sequence and its difference, and deduce closed forms, in terms of the Hessenberg determinants, and recursive relations for the Delannoy one-functional sequence, the Delannoy numbers, and central Delannoy numbers.
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