A generalized Vandermonde matrix of two sequences a and b where a is an increasing sequence of positive integers and b is an increasing sequence of nonnegative integers of the same length is the outer product of a and b with multiplication operation given by the power function. The generalized Vandermonde matrix can be implemented in the Wolfram Language as Vandermonde[a_List?VectorQ, b_List?VectorQ] := Outer[Power, a, b] /; Equal @@ Length /@ {a, b}

Vandermonde matrix

Alexandre-Théophile Vandermonde