Sequences

• A243662 → θ+1
  1 · 3, 2 · 12, 16, 3 · 55, 110, 45, 4 … Σ 1, 5, 31, 214, 1570, 11969, 93659, …
  (−∞, 0]nonnegative
• A144445 → γ
  1 · 1 · 1, 21 · 1, 203 … Σ 1, 1, 22, 204, 4663, 106548, 3404962, …
  (−∞, 0]nonnegative
• A013611 → D → D+1
  4 · 40, 32 · 108, 480, 192 · 208, 1728, 3840, 1024 … Σ 0, 4, 72, 780, 6800, 52500, 375000, …
  (−∞, 0]nonnegativerational roots
• A110441 → reverse
  1 · 1, 3 · 1, 6, 7 · 1, 9, 23, 15 … Σ 1, 4, 14, 48, 164, 560, 1912, 6528, …
  (−∞, 0]nonnegative
• A038334 → x ↦ x+1 → (θ+1)²
  400, 1280, 576 · 8000, 38400, 34560, 8192 … Σ 2256, 89152, 3324160, 119067648, …
  (−∞, 0]nonnegative
• A113214 → Veronese 2 (j=1)
  1 · 3 · 2, 1 · 0, 5 … Σ 0, 1, 3, 3, 5, 10, 14, 23, …
  (−∞, 0]nonnegative
• A266213 → Veronese 2 (j=1)
  2 · 4 · 6, 2 · 8, 12 … Σ 0, 0, 2, 4, 8, 20, 50, 120, …
  (−∞, 0]nonnegative
• A178821 → basis A013610 → x ↦ x/(x+1)
  1 · 10, 25 · 60, 300, 375 · 280, 2100, 5250, 4375 … Σ 1, 35, 735, 12005, 168070, 2117682, …
  [−1, 0]nonnegativerational roots
• A059364 → basis A013610 → x ↦ x+1
  1 · 6, 3 · 66, 69, 18 · 1056, 1698, 909, 162 … Σ 1, 9, 153, 3825, 126225, 5175225, …
  (−∞, −1]nonnegativerational roots
• A121574 → basis A013611 → x ↦ x/(x+1)
  1 · 3, 7 · 10, 48, 54 · 33, 239, 555, 413 … Σ 1, 10, 112, 1240, 13744, 152320, …
  [−1, 0]nonnegative
• A038226 → basis A007318 → basis A007318
  361, 304, 64 · 6859, 8664, 3648, 512 … Σ 729, 19683, 531441, 14348907, …
  (−∞, −1]nonnegativerational roots
• A114655 → reverse → x ↦ x+1
  2 · 6, 4 · 22, 28, 8 · 90, 168, 96, 16 … Σ 2, 10, 58, 370, 2514, 17850, 130890, …
  (−∞, −1]nonnegative
• A132774 → Veronese 2 → (θ+1)²
  1 · 2 · 0, 20 · 0, 24 … Σ 1, 2, 20, 24, 81, 90, 208, 224, …
  (−∞, 0]nonnegativerational roots
• A078812 → basis A013611 → basis A013609
  1 · 7, 8 · 48, 112, 64 · 329, 1160, 1344, 512 … Σ 1, 15, 224, 3345, 49951, 745920, …
  (−∞, 0]nonnegative
• A185410 → reverse → D
  1 · 2, 2 · 4, 20, 3 · 8, 120, 108, 4 … Σ 0, 1, 4, 27, 240, 2625, 34020, 509355, …
  (−∞, 0]nonnegative
• A088617 → basis A013609
  1 · 2, 2 · 6, 14, 8 · 22, 82, 100, 40 … Σ 1, 4, 28, 244, 2380, 24868, 272188, …
  (−∞, 0]nonnegative
• A130123 → Veronese 2 (j=1) → (θ+1)²
  2 · 0, 32 · 0, 0, 288 · 0, 0, 0, 2048 … Σ 0, 2, 0, 32, 0, 288, 0, 2048, …
  (−∞, 0]nonnegativerational roots
• A172431 → basis A013610 → θ+1
  1 · 3, 12 · 8, 60, 81 · 21, 228, 594, 432 … Σ 1, 15, 149, 1275, 10177, 78183, 586349, …
  (−∞, 0]nonnegative
• A104684 → basis A013611 → basis A013610
  1 · 7, 12 · 61, 192, 144 · 595, 2700, 3888, 1728 … Σ 1, 19, 397, 8911, 210241, 5130019, …
  (−∞, 0]nonnegative
• A053117 → x ↦ x+1 → θ+1
  1 · 2, 4 · 3, 16, 12 · 4, 40, 72, 32 … Σ 1, 6, 31, 148, 673, 2962, 12735, 53800, …
  (−∞, 0]nonnegative
• A249248 → reverse
  1 · 3, 1 · 3, 7, 1 · 3, 22, 12, 1 … Σ 1, 4, 11, 38, 131, 490, 1897, 7714, …
  (−∞, 0]nonnegative
• A060920 → reverse → x ↦ x+1
  1 · 3, 2 · 11, 15, 5 · 43, 88, 59, 13 … Σ 1, 5, 31, 203, 1345, 8933, 59359, …
  (−∞, −1]nonnegative
• Veronese parent of A109446 → x ↦ x+1
  1, 1 · 2, 1 · 4, 8, 5, 1 · 8, 12, 6, 1 … Σ 2, 3, 18, 27, 162, 243, 1458, 2187, …
  (−∞, −1]nonnegativerational roots
• A026729 → basis A008277 → (θ+1)²
  1 · 1, 4 · 2, 16, 9 · 3, 52, 72, 16 … Σ 1, 5, 27, 143, 790, 4567, 27722, …
  (−∞, 0]nonnegative
• A334218 → θ+1
  1 · 1 · 0, 4 · 0, 6, 9 … Σ 1, 1, 4, 15, 72, 420, 2880, 22680, …
  (−∞, 0]nonnegative
• A099040 → basis A013610 → x ↦ x/(x+1)
  1 · 2, 8 · 6, 42, 72 · 16, 168, 576, 640 … Σ 1, 10, 120, 1400, 16400, 192000, …
  [−1, 0]nonnegative
• A120910 → basis A013609 → D+1
  3 · 15, 6 · 63, 60, 12 · 243, 378, 180, 24 … Σ 3, 21, 135, 825, 4875, 28125, 159375, …
  (−∞, 0]nonnegativerational roots
• A197208 → D+1
  150, 180, 30 · 660, 1800, 780, 60 … Σ 360, 3300, 28980, 248136, 2090592, …
  (−∞, 0]nonnegative
• A046716 → basis A013611 → basis A007318
  1 · 6, 4 · 41, 52, 16 · 356, 644, 368, 64 … Σ 1, 10, 109, 1432, 26497, 754894, …
  (−∞, −1]nonnegative
• A024462 → basis A013611
  1 · 2, 4 · 4, 16, 16 · 16, 112, 256, 192 … Σ 1, 6, 36, 576, 9216, 147456, 2359296, …
  (−∞, 0]nonnegativerational roots
• A038231 → Veronese 2 (j=1)
  1 · 8 · 48, 1 · 256, 16 … Σ 0, 1, 8, 49, 272, 1441, 7448, 37969, …
  (−∞, 0]nonnegative
• A094638 → Veronese 2 → x ↦ x+1
  1 · 1 · 3, 2 · 12, 11 … Σ 1, 1, 5, 23, 167, 1267, 12607, 132265, …
  (−∞, −1]nonnegative
• basis-map coefficients of A026729, shifted → basis A007318 → D+1
  1 · -2, -1 · 3, 4, 1 · -4, -9, -6, -1 … Σ 1, -3, 8, -20, 48, -112, 256, -576, …
  (−∞, 0]rational roots
• A135065: A127733 * A007318 as infinite lower triangular matrices.
  1 · 4, 4 · 9, 18, 9 · 16, 48, 48, 16 … Σ 1, 8, 36, 128, 400, 1152, 3136, 8192, …
  (−∞, −1]nonnegativerational roots
• A257621 → D+1
  1 · 6, 3 · 51, 60, 9 · 420, 1179, 474, 27 … Σ 1, 9, 120, 2100, 45360, 1164240, …
  (−∞, 0]nonnegative
• A100861 → basis A013610 → basis A008277
  1 · 1 · 5, 3 · 13, 9 … Σ 1, 1, 8, 22, 217, 941, 11101, 64933, …
  (−∞, 0]nonnegative
• basis-map coefficients of A026729, shifted → basis A013610 → basis A013609
  1 · -4, -6 · 16, 48, 36 · -64, -288, -432, -216 … Σ 1, -10, 100, -1000, 10000, -100000, …
  (−∞, 0]rational roots
• A038220 → Veronese 2 → basis A008277
  1 · 3 · 13, 4 · 63, 36 … Σ 1, 3, 17, 99, 593, 3603, 22209, 138771, …
  (−∞, 0]nonnegative
• A257612 → x ↦ x+1
  1 · 4, 2 · 32, 32, 4 · 384, 576, 208, 8 … Σ 1, 6, 68, 1176, 27152, 783456, …
  (−∞, −1]nonnegative
• A100861 → basis A013611
  1 · 1 · 2, 4 · 4, 12 … Σ 1, 1, 6, 16, 106, 426, 3076, 15856, …
  (−∞, 0]nonnegative
• A097805: Number of compositions of n with k parts, T(n, k) = binomial(n-1, k-1) for n, k >= 1 and T(n, 0) = 0^n, triangle read by rows for n >= 0 and 0 <= k <=…
  1 · 0, 1 · 0, 1, 1 · 0, 1, 2, 1 … Σ 1, 1, 2, 4, 8, 16, 32, 64, …
  (−∞, 0]nonnegativerational roots
• A027467 → basis A013609 → D+1
  1 · 18, 2 · 320, 72, 4 · 5632, 1920, 216, 8 … Σ 1, 20, 396, 7776, 151632, 2939328, …
  (−∞, 0]nonnegativerational roots
• A178821 → basis A013611 → basis A013611
  1 · 30, 80 · 540, 2880, 3840 … Σ 1, 110, 7260, 372680, 16397920, …
  (−∞, 0]nonnegativerational roots
• A028326 → basis A013610 → x ↦ x/(x+1)
  2 · 4, 10 · 8, 40, 50 · 16, 120, 300, 250 … Σ 2, 14, 98, 686, 4802, 33614, 235298, …
  [−1, 0]nonnegativerational roots
• A008459 → basis A013609 → basis A013610
  1 · 4, 6 · 22, 60, 36 · 136, 540, 648, 216 … Σ 1, 10, 118, 1540, 21286, 304300, …
  (−∞, 0]nonnegative
• A130534 → D²∘x (shift +1) → θ+1
  1 · 3, 6 · 11, 36, 18 · 50, 210, 180, 40 … Σ 1, 9, 65, 480, 3829, 33439, 319976, …
  (−∞, 0]nonnegative
• A257607 → γ
  1 · 5 · 25, 10 · 125, 160 … Σ 1, 5, 35, 285, 2655, 27465, 311715, …
  (−∞, 0]nonnegative
• basis-map coefficients of A021012 → θ+1 → basis A013609
  1 · -2, -4 · 6, 24, 24 · -24, -144, -288, -192 … Σ 1, -6, 54, -648, 9720, -174960, …
  (−∞, 0]rational roots
• A111125 → basis A013610 → basis A013609
  1 · 7, 6 · 41, 78, 36 · 239, 708, 684, 216 … Σ 1, 13, 155, 1847, 22009, 262261, …
  (−∞, 0]nonnegative
• A038259 → basis A013611 → D+1
  1 · 31, 20 · 561, 1240, 400 … Σ 1, 51, 2201, 87451, 3306801, 120981251, …
  (−∞, 0]nonnegativerational roots