A111125

View A111125 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.

• A111125: Triangle read by rows: T(k,s) = ((2*k+1)/(2*s+1))*binomial(k+s,2*s), 0 <= s <= k. (identification, match triangle)
  1 · 3, 1 · 5, 5, 1 · 7, 14, 7, 1 … row sums 1, 4, 11, 29, 76, 199, 521, 1364, …
  A111125 (−4, 0) nonnegative
• A111125 → reverse (match reversed triangle)
  1 · 1, 3 · 1, 5, 5 · 1, 7, 14, 7 … row sums 1, 4, 11, 29, 76, 199, 521, 1364, …
  (−∞, 0] nonnegative
• A082985: Coefficient table for Chebyshev's U(2*n,x) polynomial expanded in decreasing powers of (-4*(1-x^2)). (match reversed triangle)
  1 · 1, 3 · 1, 5, 5 · 1, 7, 14, 7 … row sums 1, 4, 11, 29, 76, 199, 521, 1364, …
  A082985 (−∞, 0) nonnegative
• A082985 → reverse (match triangle)
  1 · 3, 1 · 5, 5, 1 · 7, 14, 7, 1 … row sums 1, 4, 11, 29, 76, 199, 521, 1364, …
  (−∞, 0] nonnegative