A051578
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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A257611: Triangle, read by rows, T(n,k) = t(n-k, k) where t(n,m) = f(m)*t(n-1,m) + f(n)*t(n,m-1) and f(n) = 2*n + 3.
(match row sums)
1 · 3, 3 · 9, 30, 9 · 27, 213, 213, 27 … row sums 1, 6, 48, 480, 5760, 80640, 1290240, …
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A028338 → basis A013611
(match row sums)
1 · 2, 4 · 8, 24, 16 · 48, 176, 192, 64 … row sums 1, 6, 48, 480, 5760, 80640, 1290240, …