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What is the inverse of a triangular matrix whose nonzero elements are binomial coefficients?...
This may answer the question, the sequence is the only implicit thing. I consider $Q=\begin{pmatrix}Q_{i,j}\end{pmatrix}_{n\times n}$ for $n\ge 3$, where
$$Q_{i,j}=
\begin{cases}
\dbinom{j}{i-1}, & 1\ …