A000407
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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A257621: Triangle read by rows: T(n, k) = t(n-k, k), where t(0,0) = 1, t(n,m) = 0 if n < 0 or m < 0, else t(n,m) = f(m)*t(n-1,m) + f(n)*t(n,m-1), and f(n) = 4*n + 3.
(match row sums)
1 · 3, 3 · 9, 42, 9 · 27, 393, 393, 27 … row sums 1, 6, 60, 840, 15120, 332640, 8648640, …
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A225471 → basis A013609
(match row sums)
1 · 4, 2 · 32, 24, 4 · 384, 352, 96, 8 … row sums 1, 6, 60, 840, 15120, 332640, 8648640, …
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A290319 → basis A013611
(match row sums)
1 · 2, 4 · 12, 32, 16 · 120, 368, 288, 64 … row sums 1, 6, 60, 840, 15120, 332640, 8648640, …