A094305

View A094305 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.

• A094305: Triangle read by rows: T(n,k) = ((n+1)(n+2)/2) * binomial(n,k) (0 <= k <= n). (identification, match reversed triangle, match triangle)
  A007318 → ×(1+(3/2)n+(1/2)n²)
  1 · 3, 3 · 6, 12, 6 · 10, 30, 30, 10 … row sums 1, 6, 24, 80, 240, 672, 1792, 4608, …
  A094305 (−∞, −1] nonnegative rational roots
• A129533: Array read by antidiagonals: T(n,k) = binomial(n+1,2)*binomial(n+k,n+1) for 0 <= k <= n. (match reversed triangle, match triangle)
  A007318 → (−1/2)D²+(−1/2+(1/2)n)D
  0, 1 · 0, 3, 3 · 0, 6, 12, 6 · 0, 10, 30, 30, 10 … row sums 0, 0, 1, 6, 24, 80, 240, 672, …
  A129533 (−∞, ∞) nonnegative rational roots