A002377

View A002377 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.

• basis-map coefficients of Triangular array of generalized Narayana numbers: T(n, k) = 2*binomial(n + 1, k + 1)*binomial(n + 1, k - 1)/(n + 1). (match row sums)
  1 · 0, 2 · -2, 2, 3 · 0, -8, 8, 4 … row sums 1, 2, 3, 4, 5, 6, 7, 8, …
  (−∞, 1]
• A053124: Triangle of coefficients of Chebyshev's U(n,2*x-1) polynomials (exponents of x in increasing order). (match row sums)
  1 · -2, 4 · 3, -16, 16 · -4, 40, -96, 64 … row sums 1, 2, 3, 4, 5, 6, 7, 8, …
  A053124 (0, 1)
• basis-map coefficients of Triangle read by rows, n>=1, 1<=k<=n, T(n,k) = k*binomial(n,k)^2/(n-k+1). (match row sums)
  1 · 0, 2 · -3, 3, 3 · 0, -12, 12, 4 … row sums 1, 2, 3, 4, 5, 6, 7, 8, …
  (−∞, 1]
• A023531 → θ+1 (match row sums)
  1 · 0, 2 · 0, 0, 3 · 0, 0, 0, 4 … row sums 1, 2, 3, 4, 5, 6, 7, 8, …
  (−∞, 0] nonnegative rational roots
• A023531 → D+1 (match row sums)
  1 · 1, 1 · 0, 2, 1 · 0, 0, 3, 1 … row sums 1, 2, 3, 4, 5, 6, 7, 8, …
  (−∞, 0] nonnegative rational roots
• A053117: Triangle read by rows of coefficients of Chebyshev's U(n,x) polynomials (exponents in increasing order). (match row sums)
  1 · 0, 2 · -1, 0, 4 · 0, -4, 0, 8 … row sums 1, 2, 3, 4, 5, 6, 7, 8, …
  A053117 (−1, 1)
• basis-map coefficients of A026729 → D+1 (match row sums)
  1 · 1, 1 · 0, 2, 1 · 0, 0, 3, 1 … row sums 1, 2, 3, 4, 5, 6, 7, 8, …
  (−∞, 0] nonnegative rational roots
• A127648: Triangle read by rows: row n consists of n zeros followed by n+1. (match row sums)
  A010054 → reverse
  1 · 0, 2 · 0, 0, 3 · 0, 0, 0, 4 … row sums 1, 2, 3, 4, 5, 6, 7, 8, …
  A127648 [−1, 0] nonnegative rational roots
• A007318 → D → γ (match row sums)
  1 · 2 · 3 · 4 … row sums 1, 2, 3, 4, 5, 6, 7, 8, …
  (−∞, 0] nonnegative rational roots
• chebyshev_u (match row sums)
  1 · 0, 2 · -1, 0, 4 · 0, -4, 0, 8 … row sums 1, 2, 3, 4, 5, 6, 7, 8, …
  (−1, 1)