A249139
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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A249139: Triangular array read by rows: row n gives the coefficients of the polynomial p(n,x) defined in Comments.
(identification, match triangle)
A011973 → x ↦ x+2 (shift +1)1 · 3, 1 · 5, 2 · 11, 7, 1 … row sums 1, 4, 7, 19, 40, 97, 217, 508, …
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A011973 → basis A007318 → x ↦ x+1
(match triangle)
1 · 1 · 3, 1 · 5, 2 … row sums 1, 1, 4, 7, 19, 40, 97, 217, …