A122704
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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A156366: Triangle of coefficients of p(n, x) where p(n, x) is defined as p(n, x) = (1-3*x)^(n+1)*PolyLog(-n, 3*x)/(3*x), read by rows.
(match row sums)
1, 12, 9 · 1, 33, 99, 27 · 1, 78, 594, 702, 81 … row sums 22, 160, 1456, 15904, 202672, 2951680, …
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A131689 → x ↦ x/(x+1)
(match row sums)
1 · 0, 1 · 0, 1, 3 · 0, 1, 8, 13 … row sums 1, 1, 4, 22, 160, 1456, 15904, 202672, …