A347056
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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A347056: Triangle read by rows: T(n,k) = (n+1)*(n+2)*(k+3)*binomial(n,k)/6, 0 <= k <= n.
(identification, match triangle)
A007318 → (1/3+(1/2)n+(1/6)n²)θ+1+(3/2)n+(1/2)n²1 · 3, 4 · 6, 16, 10 · 10, 40, 50, 20 … row sums 1, 7, 32, 120, 400, 1232, 3584, 9984, …
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A007318 → (1/3+(1/2)n+(1/6)n²)θ+1+(3/2)n+(1/2)n² → reverse
(match reversed triangle)
1 · 4, 3 · 10, 16, 6 · 20, 50, 40, 10 … row sums 1, 7, 32, 120, 400, 1232, 3584, 9984, …