A142967
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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A142963: Triangle read by rows, coefficients of the polynomials P(k, x) = (1/2) Sum_{p=0..k-1} Stirling2(k, p+1)*x^p*(1-4*x)^(k-1-p)*(2*p+2)!/(p+1)!.
(match row sums)
1 · 1, 2 · 1, 10, 4 · 1, 30, 72, 8 … row sums 1, 3, 15, 111, 1071, 12663, 177255, …