A059364
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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A059364: Triangle T(n,k)=Sum_{i=0..n} |stirling1(n,n-i)|*binomial(i,k), k=0..n-1.
(identification, match triangle)
1 · 2, 1 · 6, 7, 2 · 24, 46, 29, 6 … row sums 1, 3, 15, 105, 945, 10395, 135135, …
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A130534 → x ↦ x/(x+1)
(match reversed triangle)
1 · 1, 2 · 2, 7, 6 · 6, 29, 46, 24 … row sums 1, 3, 15, 105, 945, 10395, 135135, …
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A088996: Triangle T(n, k) read by rows: T(n, k) = Sum_{j=0..n} binomial(j, n-k) * |Stirling1(n, n-j)|.
(match reversed triangle)
1 · 0, 1 · 0, 1, 2 · 0, 2, 7, 6 … row sums 1, 1, 3, 15, 105, 945, 10395, 135135, …