A123125
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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A123125: Triangle of Eulerian numbers T(n,k), 0 <= k <= n, read by rows.
(identification, match triangle)
A173018 → reverse (shift +1)1 · 0, 1 · 0, 1, 1 · 0, 1, 4, 1 … row sums 1, 1, 2, 6, 24, 120, 720, 5040, …