A051523
identification: the entry's rule defines the sequence for every index; tail: the sequence is the entry's tail after some prefix rows; match_*: finite agreement only.
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A051523: Generalized Stirling number triangle of first kind read by rows: T(n, k) = [x^k] Product_{m=1..n} (x - m - r), with r = 9.
(identification, match triangle)
A028338 → x ↦ −2x+191 · -10, 1 · 110, -21, 1 · -1320, 362, -33, 1 … row sums 1, -9, 90, -990, 11880, -154440, …