Recurrence relation

Stirling number

Difference polynomials

Pure mathematics

Biology

Classical orthogonal polynomials

Genetics

Sequence (biology)

Mathematics

Binomial coefficient

Bell polynomials

Macdonald polynomials

Combinatorics

Gegenbauer polynomials

Algebra over a field

Wilson polynomials

Discrete orthogonal polynomials

Hahn polynomials

Orthogonal polynomials

Revista de la Real Academia de Ciencias Exactas Físicas y Naturales Serie A Matemáticas

In the paper, by virtue of (1) the Stirling inversion theorem and the binomial inversion theorem, (2) the Faà di Bruno formula and two identities for the Bell polynomials of the second kind, (3) a formula of higher order derivative for the ratio of two differentiable functions, the authors (1) present two explicit formulas, a determinantal expression, and a recursive relation for a sequence of unnamed polynomials, (2) derive two identities connecting the sequence of unnamed polynomials with the Bell polynomials, (3) recover a known identity connecting the sequence of unnamed polynomials with the Bell polynomials.

Some identities for a sequence of unnamed polynomials connected with the Bell polynomials