A019538

View A019538 at the OEIS

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.

• A019538: Triangle of numbers T(n,k) = k!*Stirling2(n,k) read by rows (n >= 1, 1 <= k <= n). (identification, match triangle)
  1 · 1, 2 · 1, 6, 6 · 1, 14, 36, 24 … row sums 1, 3, 13, 75, 541, 4683, 47293, 545835, …
  A019538 (−1, 0) nonnegative
• A090582: T(n, k) = Sum_{j=0..n-k} (-1)^j*binomial(n - k + 1, j)*(n - k + 1 - j)^n. Triangle read by rows, T(n, k) for 1 <= k <= n. (match reversed triangle)
  1 · 2, 1 · 6, 6, 1 · 24, 36, 14, 1 … row sums 1, 3, 13, 75, 541, 4683, 47293, 545835, …
  A090582 (−∞, 0] nonnegative
• A008292 → x ↦ x+1 (match reversed triangle)
  1 · 2, 1 · 6, 6, 1 · 24, 36, 14, 1 … row sums 1, 3, 13, 75, 541, 4683, 47293, 545835, …
  (−∞, −1] nonnegative
• A131689 → reverse (match reversed triangle)
  1 · 1 · 2, 1 · 6, 6, 1 … row sums 1, 1, 3, 13, 75, 541, 4683, 47293, …
  (−∞, −1] nonnegative
• A131689: Triangle of numbers T(n,k) = k!*Stirling2(n,k) = A000142(k)*A048993(n,k) read by rows, T(n, k) for 0 <= k <= n. (match triangle)
  1 · 0, 1 · 0, 1, 2 · 0, 1, 6, 6 … row sums 1, 1, 3, 13, 75, 541, 4683, 47293, …
  A131689 (−1, 0] nonnegative
• A173018 → reverse (shift +1) → x ↦ x/(x+1) (match triangle)
  1 · 0, 1 · 0, 1, 2 · 0, 1, 6, 6 … row sums 1, 1, 3, 13, 75, 541, 4683, 47293, …
  [−1, 0] nonnegative