preserver_image / euler_polynomial, shift 0

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352 sequences

• A100862 → θ+1
  1 · 1, 2 · 1, 6, 3 · 1, 12, 18, 4 … row sums 1, 3, 10, 35, 129, 497, 1996, 8325, …
  (−∞, 0] nonnegative
• delannoy → (θ+1)²
  1 · 1, 4 · 1, 12, 9 · 1, 20, 45, 16 … row sums 1, 5, 22, 82, 283, 923, 2892, 8788, …
  (−∞, 0] nonnegative
• A023531 → 2D+1 → (θ+1)²
  1 · 2, 4 · 0, 16, 9 · 0, 0, 54, 16 … row sums 1, 6, 25, 70, 153, 286, 481, 750, …
  (−∞, 0] nonnegative rational roots
• A133080 → (θ+1)²
  1 · 1, 4 · 0, 0, 9 · 0, 0, 9, 16 … row sums 1, 5, 9, 25, 25, 61, 49, 113, …
  (−∞, 0] nonnegative rational roots
• A100861 → θ+1
  1 · 1 · 1, 2 · 1, 6 … row sums 1, 1, 3, 7, 22, 66, 226, 778, …
  (−∞, 0] nonnegative
• A172431 → θ+1
  1 · 1, 4 · 1, 8, 9 · 1, 12, 30, 16 … row sums 1, 5, 18, 59, 185, 564, 1685, 4957, …
  (−∞, 0] nonnegative
• A173018 → reverse (shift +1) → (θ+1)²
  1 · 0, 4 · 0, 4, 9 · 0, 4, 36, 16 … row sums 1, 4, 13, 56, 304, 1980, 15000, 129360, …
  (−∞, 0] nonnegative
• A010054 → reverse → θ+1
  1 · 0, 4 · 0, 0, 9 · 0, 0, 0, 16 … row sums 0, 1, 4, 9, 16, 25, 36, 49, …
  (−∞, 0] nonnegative rational roots
• A106800 → reverse (shift +1) → θ+1
  1 · 0, 2 · 0, 2, 3 · 0, 2, 9, 4 … row sums 1, 2, 5, 15, 52, 203, 877, 4140, …
  (−∞, 0] nonnegative
• A008288 → (θ+1)²
  1 · 1, 4 · 1, 12, 9 · 1, 20, 45, 16 … row sums 1, 5, 22, 82, 283, 923, 2892, 8788, …
  (−∞, 0] nonnegative
• A106800 → reverse (shift +1) → (θ+1)²
  1 · 0, 4 · 0, 4, 9 · 0, 4, 27, 16 … row sums 1, 4, 13, 47, 188, 825, 3937, 20270, …
  (−∞, 0] nonnegative
• A128099 → θ+1
  1 · 1 · 1, 4 · 1, 8 … row sums 1, 1, 5, 9, 25, 53, 125, 273, …
  (−∞, 0] nonnegative
• A013610 → (θ+1)²
  1 · 1, 12 · 1, 24, 81 · 1, 36, 243, 432 … row sums 1, 13, 106, 712, 4288, 24064, 128512, …
  (−∞, 0] nonnegative
• A008278 → θ+1
  1 · 1, 2 · 1, 6, 3 · 1, 12, 21, 4 … row sums 1, 3, 10, 38, 161, 747, 3753, 20253, …
  (−∞, 0] nonnegative
• A188440 → (θ+1)²
  1 · 1 · 1, 8 · 1, 8 … row sums 1, 1, 9, 9, 53, 53, 261, 261, …
  (−∞, 0] nonnegative
• A334218 → (θ+1)²
  1 · 1 · 0, 8 · 0, 12, 27 … row sums 1, 1, 8, 39, 224, 1520, 11880, 105000, …
  (−∞, 0] nonnegative
• A008292 → γ (scale 1/4) (shift +1) → (θ+1)²
  1 · 2 · 4, 8 · 8, 64 … row sums 1, 2, 12, 72, 512, 4144, 37632, 379008, …
  (−∞, 0] nonnegative
• A007318 → ×(1+(3/2)n+(1/2)n²) → θ+1
  1 · 3, 6 · 6, 24, 18 · 10, 60, 90, 40 … row sums 1, 9, 48, 200, 720, 2352, 7168, 20736, …
  (−∞, 0] nonnegative rational roots
• A207607 → θ+1
  1 · 1, 4 · 1, 10, 6 · 1, 18, 27, 8 … row sums 1, 5, 17, 54, 166, 499, 1475, 4303, …
  (−∞, 0] nonnegative
• A249251 → (θ+1)²
  1 · 1, 12 · 1, 24, 54 · 1, 36, 189, 192 … row sums 1, 13, 79, 418, 2014, 9127, 39583, …
  (−∞, 0] nonnegative
• A026729 → θ+1
  1 · 0, 2 · 0, 2, 3 · 0, 0, 6, 4 … row sums 1, 2, 5, 10, 20, 38, 71, 130, …
  (−∞, 0] nonnegative
• A081582 → θ+1
  1 · 1, 2 · 1, 18, 3 · 1, 34, 51, 4 … row sums 1, 3, 22, 90, 447, 1925, 8572, 36612, …
  (−∞, 0] nonnegative
• A007318 → (θ+1)² → (θ+1)²
  1 · 1, 16 · 1, 32, 81 · 1, 48, 243, 256 … row sums 1, 17, 114, 548, 2200, 7872, 25984, …
  (−∞, 0] nonnegative
• A038208 → θ+1
  1 · 2, 4 · 4, 16, 12 · 8, 48, 72, 32 … row sums 1, 6, 32, 160, 768, 3584, 16384, 73728, …
  (−∞, 0] nonnegative rational roots
• A124932: Triangle read by rows: T(n,k) = k*(k+1)*binomial(n,k)/2 (1 <= k <= n).
  A007318 → (1/2+(1/2)n)θ+1+n
  1 · 2, 3 · 3, 9, 6 · 4, 18, 24, 10 … row sums 1, 5, 18, 56, 160, 432, 1120, 2816, …
  A124932 (−∞, 0] nonnegative rational roots
• A126216 → θ+1
  1 · 2, 2 · 5, 10, 3 · 14, 42, 27, 4 … row sums 1, 4, 18, 87, 439, 2278, 12052, 64669, …
  (−∞, 0] nonnegative
• A023531 → θ+1
  1 · 0, 2 · 0, 0, 3 · 0, 0, 0, 4 … row sums 1, 2, 3, 4, 5, 6, 7, 8, …
  (−∞, 0] nonnegative rational roots
• A033282 → θ+1
  1 · 1, 4 · 1, 10, 15 · 1, 18, 63, 56 … row sums 1, 5, 26, 138, 743, 4043, 22180, …
  (−∞, 0] nonnegative
• A091044 → θ+1
  1 · 2, 4 · 3, 20, 9 · 4, 56, 84, 16 … row sums 1, 6, 32, 160, 768, 3584, 16384, 73728, …
  (−∞, 0] nonnegative
• A055356 → θ+1
  1 · 1 · 1, 2 · 1, 8, 6 … row sums 1, 1, 3, 15, 101, 851, 8603, 101423, …
  (−∞, 0] nonnegative
• A130123 → (θ+1)²
  1 · 0, 8 · 0, 0, 36 · 0, 0, 0, 128 … row sums 1, 8, 36, 128, 400, 1152, 3136, 8192, …
  (−∞, 0] nonnegative rational roots
• A094305: Triangle read by rows: T(n,k) = ((n+1)(n+2)/2) * binomial(n,k) (0 <= k <= n).
  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
• A114655 → θ+1
  2 · 4, 4 · 8, 24, 6 · 16, 96, 72, 8 … row sums 2, 8, 38, 192, 1002, 5336, 28814, …
  (−∞, 0] nonnegative
• A103406: Triangle read by rows: n-th row = unsigned coefficients of the characteristic polynomials of an n X n matrix with 2's on the diagonal and 1's elsewhere.
  A007318 → θ+1
  1 · 1, 2 · 1, 4, 3 · 1, 6, 9, 4 … row sums 1, 3, 8, 20, 48, 112, 256, 576, …
  A103406 (−∞, 0] nonnegative rational roots
• A249252 → (θ+1)²
  1 · 1, 16 · 1, 32, 72 · 1, 48, 288, 256 … row sums 1, 17, 105, 593, 3049, 14801, 68873, …
  (−∞, 0] nonnegative
• A133087 → θ+1
  1 · 2, 2 · 1, 4, 3 · 2, 10, 12, 4 … row sums 1, 4, 8, 28, 48, 160, 256, 832, …
  (−∞, 0] nonnegative
• A178822 → (θ+1)²
  1 · 6, 24 · 21, 168, 189 · 56, 672, 1512, 896 … row sums 1, 30, 378, 3136, 20160, 108864, …
  (−∞, 0] nonnegative
• A059473 → (θ+1)²
  1 · 2, 8 · 4, 40, 36 · 8, 128, 288, 128 … row sums 1, 10, 80, 552, 3508, 21080, 121664, …
  (−∞, 0] nonnegative
• A030528 → θ+1
  1 · 1, 2 · 0, 4, 3 · 0, 2, 9, 4 … row sums 1, 3, 7, 15, 30, 58, 109, 201, …
  (−∞, 0] nonnegative
• A178820 → (θ+1)²
  1 · 4, 16 · 10, 80, 90 · 20, 240, 540, 320 … row sums 1, 20, 180, 1120, 5600, 24192, 94080, …
  (−∞, 0] nonnegative
• basis-map coefficients of A026729 → (θ+1)²
  1 · 0, 4 · 0, 0, 9 · 0, 0, 0, 16 … row sums 1, 4, 9, 16, 25, 36, 49, 64, …
  (−∞, 0] nonnegative rational roots
• A102662 → θ+1
  1 · 1, 6 · 1, 10, 9 · 1, 14, 33, 12 … row sums 1, 7, 20, 60, 171, 477, 1306, 3526, …
  (−∞, 0] nonnegative
• A116414 → (θ+1)²
  1 · 4, 4 · 13, 32, 9 · 40, 168, 108, 16 … row sums 1, 8, 54, 332, 1921, 10656, 57301, …
  (−∞, 0] nonnegative
• A391403: Triangle read by rows: T(n,k) is k-th entry of the gamma-vector of the n-dimensional cyclohedron, 0 <= k <= floor(n/2).
  A011973 → ⊙ C(n,k)
  1 · 1 · 1, 2 · 1, 6 … row sums 1, 1, 3, 7, 19, 51, 141, 393, …
  A391403 (−∞, 0] nonnegative
• A122431 → θ+1
  1, 6, 9, 4 · 0, 2, 9, 12, 5 · 0, 0, 3, 12, 15, 6 … row sums 20, 28, 36, 44, 52, 60, 68, 76, …
  (−∞, 0] nonnegative rational roots
• A063967 → (θ+1)²
  1 · 1, 4 · 2, 12, 9 · 3, 28, 45, 16 … row sums 1, 5, 23, 92, 346, 1240, 4296, 14496, …
  (−∞, 0] nonnegative
• A110441 → (θ+1)²
  1 · 3, 4 · 7, 24, 9 · 15, 92, 81, 16 … row sums 1, 7, 40, 204, 968, 4372, 19048, 80736, …
  (−∞, 0] nonnegative
• A272866 → θ+1
  1 · 1, 6, 3 · 1, 12, 33, 24, 5 … row sums 1, 10, 75, 500, 3125, 18750, 109375, …
  (−∞, 0] nonnegative
• A104684 → θ+1
  1 · 2, 2 · 6, 12, 3 · 20, 60, 36, 4 … row sums 1, 4, 21, 120, 705, 4188, 24997, …
  (−∞, 0] nonnegative
• A010054 → reverse → θ+1
  1 · 0, 6 · 0, 0, 18 · 0, 0, 0, 40 … row sums 1, 6, 18, 40, 75, 126, 196, 288, …
  (−∞, 0] nonnegative rational roots