We introduce a triangular array of integers defined by a(n, k) = k(k + 1)n−k
for n ≥ 1
and 1 ≤ k ≤ n, which we call the researcher’s triangle. The construction is multiplicative and
differs from classical additive triangles such as Pascal’s. We give combinatorial interpretations
using a leaders-followers model and a rooted hierarchical structure model. We identify several
diagonal sequences as classical figurate numbers, including powers of two (A000079), natural
numbers (A000027), and oblong numbers (A002378), and establish connections to triangular
and tetrahedral numbers. We derive a bivariate generating function and a recurrence relation,
and we discuss the row sums.