Identities in Iterated Rascal Triangles

In this manuscript, we introduce new binomial identities in iterated Rascal triangles, uncovering a connection between Vandermonde convolution and iterated Rascal numbers. Additionally, we present novel identities involving the finite differences of iterated Rascal numbers and binomial coefficients. The manuscript also offers a proof of the row sums conjecture for iterated Rascal triangles. Furthermore, we establish and explore the relationship between iterated Rascal triangles and $(1,q)$-binomial coefficients, highlighting connections to relevant OEIS sequences. All results are supported by supplementary Mathematica programs for validation.

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