A104150

View A104150 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.

• A154986: Triangle T(n, k) = coefficients of p(x, n) where p(x,n) = (x+1)*p(x, n-1) + n*(n-1)*x*p(x, n-2), read by rows. (match row sums)
  1 · 1, 1 · 1, 4, 1 · 1, 11, 11, 1 … row sums 1, 2, 6, 24, 120, 720, 5040, 40320, …
  A154986 (−∞, 0) nonnegative
• A008303: Triangle read by rows: T(n,k) (n >= 1, 0 <= k <= ceiling(n/2)-1) = number of permutations of [n] with k peaks. (match row sums)
  A008292 → γ (scale 1/4) (shift +1)
  1 · 2 · 4, 2 · 8, 16 … row sums 1, 2, 6, 24, 120, 720, 5040, 40320, …
  A008303 (−∞, 0] nonnegative
• A137320 → reverse (match row sums)
  1 · 2 · 4, 2 · 8, 12, 4 … row sums 1, 2, 6, 24, 120, 720, 5040, 40320, …
  (−∞, 0] nonnegative rational roots
• A334218: Triangle read by rows: T(n,k) is the number of permutations of 1..n arranged in a circle with exactly k descents. (match row sums)
  1 · 1 · 0, 2 · 0, 3, 3 … row sums 1, 1, 2, 6, 24, 120, 720, 5040, …
  A334218 (−∞, 0] nonnegative
• A156992 → γ (match row sums)
  1 · 2 · 6 · 24 … row sums 1, 2, 6, 24, 120, 720, 5040, 40320, …
  (−∞, 0] nonnegative rational roots
• A094638: Triangle read by rows: T(n,k) = |s(n,n+1-k)|, where s(n,k) are the signed Stirling numbers of the first kind A008276 (1 <= k <= n; in other words, the unsigned Stirling numbers of the first … (match row sums)
  1 · 1, 1 · 1, 3, 2 · 1, 6, 11, 6 … row sums 1, 2, 6, 24, 120, 720, 5040, 40320, …
  A094638 (−∞, 0) nonnegative rational roots
• A008971: Triangle read by rows: T(n,k) is the number of permutations of [n] with k increasing runs of length at least 2. (match row sums)
  type_b_eulerian → γ (scale 1/4)
  1 · 1 · 1, 1 · 1, 5 … row sums 1, 1, 2, 6, 24, 120, 720, 5040, …
  A008971 (−∞, 0] nonnegative
• A137320: Coefficients of raising factorial polynomials, T(n,k) = [x^k] p(x, n) where p(x, n) = (m*x + n - 1)*p(x, n - 1) with p[x, 0] = 1, p[x, -1] = 0, p[x, 1] = m*x and m = 2. Triangle read by rows… (match row sums)
  1 · 0, 2 · 0, 2, 4 · 0, 4, 12, 8 … row sums 1, 2, 6, 24, 120, 720, 5040, 40320, …
  A137320 (−∞, 0] nonnegative rational roots
• A196347 → γ (match row sums)
  1 · 1 · 2 · 6 … row sums 1, 1, 2, 6, 24, 120, 720, 5040, …
  (−∞, 0] nonnegative rational roots
• A173018 → reverse (shift +1) → reverse (match row sums)
  1 · 1 · 1, 1 · 1, 4, 1 … row sums 1, 1, 2, 6, 24, 120, 720, 5040, …
  (−∞, 0] nonnegative
• A008292 → γ (scale 1/4) (match row sums)
  1 · 2 · 4, 2 · 8, 16 … row sums 1, 2, 6, 24, 120, 720, 5040, 40320, …
  (−∞, 0] nonnegative
• A136572 → D+1 (match row sums)
  1 · 1, 1 · 0, 4, 2 · 0, 0, 18, 6 … row sums 1, 2, 6, 24, 120, 720, 5040, 40320, …
  (−∞, 0] nonnegative rational roots
• A132393 → reverse (match row sums)
  1 · 1 · 1, 1 · 1, 3, 2 … row sums 1, 1, 2, 6, 24, 120, 720, 5040, …
  (−∞, 0] nonnegative rational roots
• A136572 → θ+1 (match row sums)
  1 · 0, 2 · 0, 0, 6 · 0, 0, 0, 24 … row sums 1, 2, 6, 24, 120, 720, 5040, 40320, …
  (−∞, 0] nonnegative rational roots
• A132393: Triangle of unsigned Stirling numbers of the first kind (see A048994), read by rows, T(n,k) for 0 <= k <= n. (match row sums)
  1 · 0, 1 · 0, 1, 1 · 0, 2, 3, 1 … row sums 1, 1, 2, 6, 24, 120, 720, 5040, …
  A132393 (−∞, 0] nonnegative rational roots
• A123125: Triangle of Eulerian numbers T(n,k), 0 <= k <= n, read by rows. (match row sums)
  A173018 → reverse (shift +1)
  1 · 0, 1 · 0, 1, 1 · 0, 1, 4, 1 … row sums 1, 1, 2, 6, 24, 120, 720, 5040, …
  A123125 (−∞, 0] nonnegative
• A173018: Euler's triangle: triangle of Eulerian numbers T(n,k) (n>=0, 0 <= k <= n) read by rows. (match row sums)
  1 · 1 · 1, 1 · 1, 4, 1 … row sums 1, 1, 2, 6, 24, 120, 720, 5040, …
  A173018 (−∞, 0) nonnegative
• A130534: Triangle T(n,k), 0 <= k <= n, read by rows, giving coefficients of the polynomial (x+1)(x+2)...(x+n), expanded in increasing powers of x. T(n,k) is also the unsigned Stirling number |s(n+1, … (match row sums)
  1 · 1, 1 · 2, 3, 1 · 6, 11, 6, 1 … row sums 1, 2, 6, 24, 120, 720, 5040, 40320, …
  A130534 (−∞, −1] nonnegative rational roots
• A136572: Triangle read by rows: row n consists of n zeros followed by n!. (match row sums)
  1 · 0, 1 · 0, 0, 2 · 0, 0, 0, 6 … row sums 1, 1, 2, 6, 24, 120, 720, 5040, …
  A136572 [−1, 0] nonnegative rational roots
• A008292: Eulerian (match row sums)
  1 · 1, 1 · 1, 4, 1 · 1, 11, 11, 1 … row sums 1, 2, 6, 24, 120, 720, 5040, 40320, …
  A008292 (−∞, 0) nonnegative