A051338
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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A051338: Generalized Stirling number triangle of first kind read by rows: T(n, k) = [x^k] Product_{m=1..n} (x - m - r), with r = 5.
(identification, match triangle)
A028338 → x ↦ −2x+111 · -6, 1 · 42, -13, 1 · -336, 146, -21, 1 … row sums 1, -5, 30, -210, 1680, -15120, 151200, …