definition_equality

All-n equality of two definitions. All operations

163 sequences

• A011973 → x ↦ x+2 (shift +1) → basis A007318
  1 · 4, 1 · 7, 2 · 19, 9, 1 … row sums 1, 5, 9, 29, 65, 181, 441, 1165, …
  (−∞, −1] nonnegative
• A125092: Triangle read by rows: T(n,k) = (k+1)^2*binomial(n,k) (0 <= k <= n).
  A007318 → (θ+1)²
  1 · 1, 4 · 1, 8, 9 · 1, 12, 27, 16 … row sums 1, 5, 18, 56, 160, 432, 1120, 2816, …
  A125092 (−∞, 0] nonnegative
• A078812 → basis A007318
  1 · 3, 1 · 8, 6, 1 · 21, 25, 9, 1 … row sums 1, 4, 15, 56, 209, 780, 2911, 10864, …
  (−5, −1) nonnegative
• A081579: Pascal-(1,4,1) array.
  1 · 1, 1 · 1, 6, 1 · 1, 11, 11, 1 … row sums 1, 2, 8, 24, 80, 256, 832, 2688, …
  A081579 (−∞, 0) nonnegative
• A093375: Array T(m,n) read by ascending antidiagonals: T(m,n) = m*binomial(n+m-2, n-1) for m, n >= 1.
  A007318 → D+1
  1 · 2, 1 · 3, 4, 1 · 4, 9, 6, 1 … row sums 1, 3, 8, 20, 48, 112, 256, 576, …
  A093375 (−∞, 0] nonnegative rational roots
• A081577: Pascal-(1,2,1) array read by antidiagonals.
  1 · 1, 1 · 1, 4, 1 · 1, 7, 7, 1 … row sums 1, 2, 6, 16, 44, 120, 328, 896, …
  A081577 (−∞, 0) nonnegative
• A132774: A natural number operator.
  A023531 → 2D+1+2n
  1 · 2, 3 · 0, 4, 5 · 0, 0, 6, 7 … row sums 1, 5, 9, 13, 17, 21, 25, 29, …
  A132774 [−1, 0] nonnegative rational roots
• A099040: Riordan array (1, 2+2x).
  1 · 0, 2 · 0, 2, 4 · 0, 0, 8, 8 … row sums 1, 2, 6, 16, 44, 120, 328, 896, …
  A099040 (−2, 0] nonnegative
• A086645: Triangle read by rows: T(n, k) = binomial(2n, 2k).
  1 · 1, 1 · 1, 6, 1 · 1, 15, 15, 1 … row sums 1, 2, 8, 32, 128, 512, 2048, 8192, …
  A086645 (−∞, 0) nonnegative
• A060920: Bisection of Fibonacci triangle A037027: even-indexed members of column sequences of A037027 (not counting leading zeros).
  1 · 2, 1 · 5, 5, 1 · 13, 20, 9, 1 … row sums 1, 3, 11, 43, 171, 683, 2731, 10923, …
  A060920 (−∞, −1] nonnegative
• A113214 → basis A007318
  1 · 3, 1 · 4, 5, 1 · 7, 13, 7, 1 … row sums 1, 4, 10, 28, 76, 208, 568, 1552, …
  (−∞, −1] nonnegative
• A136572: Triangle read by rows: row n consists of n zeros followed by n!.
  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
• A011973 → basis A007318 → x ↦ x+1
  1 · 1 · 3, 1 · 5, 2 … row sums 1, 1, 4, 7, 19, 40, 97, 217, …
  (−∞, −1] nonnegative