A051339
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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A051339: Generalized Stirling number triangle of first kind read by rows: T(n, k) = [x^k] Product_{m=1..n} (x - m - r), with r = 6.
(identification, match triangle)
A028338 → x ↦ −2x+131 · -7, 1 · 56, -15, 1 · -504, 191, -24, 1 … row sums 1, -6, 42, -336, 3024, -30240, 332640, …