Sequences

• A038322 → basis A007318 → x ↦ x+1
  1 · 27, 8 · 729, 432, 64 · 19683, 17496, 5184, 512 … Σ 1, 35, 1225, 42875, 1500625, 52521875, …
  (−∞, −1]nonnegativerational roots
• A154233 → x ↦ x/(x+1)
  1 · 1, 2 · 1, 9, 9 · 1, 22, 60, 40 … Σ 1, 3, 19, 123, 1091, 10407, 120683, …
  [−1, 0]nonnegative
• A084950 → D
  1 · 4 · 18, 2 · 96, 18 … Σ 0, 1, 4, 20, 114, 747, 5568, 46684, …
  (−∞, 0]nonnegative
• A207824 → x ↦ x+1 → x ↦ x+1
  1 · 7, 1 · 48, 14, 1 · 329, 145, 21, 1 … Σ 1, 8, 63, 496, 3905, 30744, 242047, …
  (−9, −5)nonnegative
• basis-map coefficients of A026729, shifted → basis A013610 → basis A013611
  1 · -4, -12 · 16, 96, 144 · -64, -576, -1728, -1728 … Σ 1, -16, 256, -4096, 65536, -1048576, …
  (−∞, 0]rational roots
• A038271 → basis A013611 → D+1
  1 · 32, 20 · 624, 1280, 400 … Σ 1, 52, 2304, 94208, 3670016, 138412032, …
  (−∞, 0]nonnegativerational roots
• A106246 → θ+1 → (θ+1)²
  1 · 2, 8 · 1, 32, 27 · 0, 24, 162, 64 … Σ 1, 10, 60, 250, 799, 2106, 4810, 9850, …
  (−∞, 0]nonnegative
• A056241 → basis A013611
  1 · 2, 4 · 5, 20, 16 · 14, 84, 144, 64 … Σ 1, 6, 41, 306, 2401, 19326, 157481, …
  (−∞, 0]nonnegative
• A081580 → basis A013611 → basis A013610
  1 · 6, 12 · 61, 204, 144 · 516, 2616, 4032, 1728 … Σ 1, 18, 409, 8892, 194821, 4262598, …
  (−∞, 0]nonnegative
• A380860: Triangle read by rows: T(n,m) (0<=m<=n) = number of positive n-digit numbers that have exactly m copies of a specific, previously selected positive ba…
  1 · 8, 1 · 72, 17, 1 · 648, 225, 26, 1 … Σ 1, 9, 90, 900, 9000, 90000, 900000, …
  (−∞, 0)nonnegativerational roots
• A026374 → x ↦ x+1
  1 · 2, 1 · 5, 5, 1 · 10, 15, 7, 1 … Σ 1, 3, 11, 33, 121, 363, 1331, 3993, …
  (−∞, −1]nonnegative
• A038326 → basis A013611
  1 · 23, 48 · 529, 2208, 2304 … Σ 1, 71, 5041, 357911, 25411681, …
  (−∞, 0]nonnegativerational roots
• A038281 → θ+1
  64, 96, 27 · 512, 1152, 648, 108 … Σ 187, 2420, 30613, 380666, 4670479, …
  (−∞, 0]nonnegativerational roots
• A241171 → θ+1
  1 · 1, 12 · 1, 60, 270 · 1, 252, 3780, 10080 … Σ 1, 13, 331, 14113, 910111, 82795813, …
  (−∞, 0]nonnegative
• A033282 → D+1
  1 · 3, 2 · 6, 15, 5 · 10, 51, 63, 14 … Σ 1, 5, 26, 138, 743, 4043, 22180, …
  (−∞, 0]nonnegative
• A091044 → basis A013610 → basis A008277
  1 · 10, 6 · 91, 129, 27 · 820, 2124, 1008, 108 … Σ 1, 16, 247, 4060, 71908, 1368598, …
  (−∞, 0]nonnegative
• A145596 → x ↦ x+1
  1 · 4, 2 · 14, 14, 3 · 48, 72, 32, 4 … Σ 1, 6, 31, 156, 785, 3978, 20335, …
  (−∞, −1]nonnegative
• A110441 → reverse → D+1
  1 · 4, 3 · 7, 20, 7 · 10, 55, 68, 15 … Σ 1, 7, 34, 148, 612, 2452, 9608, 37024, …
  (−∞, 0]nonnegative
• A027467 → basis A013611 → D
  4 · 128, 32 · 3072, 1536, 192 … Σ 0, 4, 160, 4800, 128000, 3200000, …
  (−∞, 0]nonnegativerational roots
• A026729 → basis A008277 → x ↦ x/(x+1)
  1 · 1, 2 · 2, 8, 7 · 3, 22, 43, 25 … Σ 1, 3, 17, 93, 595, 4183, 32249, 269277, …
  [−1, 0]nonnegative
• A131222 → (θ+1)²
  1 · 0, 4 · 0, 12, 9 · 0, 56, 81, 16 … Σ 1, 4, 21, 153, 1420, 15992, 211700, …
  (−∞, 0]nonnegative
• A154986 → x ↦ x+1
  1 · 2, 1 · 6, 6, 1 · 24, 36, 14, 1 … Σ 1, 3, 13, 75, 537, 4611, 46053, 525483, …
  (−∞, −1]nonnegative
• A290595 → (θ+1)²
  1 · 1, 8 · 4, 76, 36 · 28, 888, 1323, 128 … Σ 1, 9, 116, 2367, 64800, 2208465, …
  (−∞, 0]nonnegative
• A178820 → basis A007318 → θ+1
  1 · 8, 8 · 40, 80, 30 · 160, 480, 360, 80 … Σ 1, 16, 150, 1080, 6615, 36288, 183708, …
  (−∞, 0]nonnegativerational roots
• A099040 → basis A013611 → basis A013610
  1 · 10, 24 · 110, 504, 576 · 1200, 8160, 18432, 13824 … Σ 1, 34, 1190, 41616, 1455404, 50898680, …
  (−∞, 0]nonnegative
• A124932 → basis A007318 → x ↦ x/(x+1)
  1 · 5, 8 · 18, 57, 45 · 56, 264, 414, 216 … Σ 1, 13, 120, 950, 6875, 46875, 306250, …
  [−1, 0]nonnegativerational roots
• A008277: Triangle of Stirling numbers of the second kind, S2(n,k), n >= 1, 1 <= k <= n.
  1 · 1, 1 · 1, 3, 1 · 1, 7, 6, 1 … Σ 1, 2, 5, 15, 52, 203, 877, 4140, …
  (−∞, 0)nonnegative
• A269944 → x ↦ x+1 → θ+1
  1 · 1, 2 · 2, 6, 3 · 10, 34, 24, 4 … Σ 1, 3, 11, 72, 828, 15300, 420228, …
  (−∞, 0]nonnegative
• A249250 → reverse
  1 · 3, 1 · 3, 6, 1 · 3, 15, 9, 1 … Σ 1, 4, 10, 28, 76, 208, 568, 1552, …
  (−∞, 0]nonnegative
• basis-map coefficients of A113214, shifted → basis A013609 → (θ+1)²
  1 · -2, -8 · 4, 32, 36 · -8, -96, -216, -128 … Σ 1, -10, 72, -448, 2560, -13824, 71680, …
  (−∞, 0]
• basis-map coefficients of Square array of binomial coefficients T(n,k) = binomial(n,k), n >= 0, k >= 0, read by downward antidiagonals. shifted by x -> -x + 0
  1 · 0, -1 · 0, 0, 1 · 0, 0, 0, -1 … Σ 1, -1, 1, -1, 1, -1, 1, -1, …
  [−1, 0]rational roots
• A038329 → basis A013610
  225, 270, 81 · 3375, 6075, 3645, 729 … Σ 576, 13824, 331776, 7962624, 191102976, …
  (−∞, 0]nonnegativerational roots
• A163626 → Pₙ + Pₙ₊₁
  2, -1 · 2, -4, 2 · 2, -10, 14, -6 … Σ 1, 0, 0, 0, 0, 0, 0, 0, …
  (−∞, ∞)
• A304236 → D+1
  1 · 1 · 4, 3 · 7, 6 … Σ 1, 1, 7, 13, 46, 106, 301, 739, …
  (−∞, 0]nonnegative
• A145324 → basis A007318 → (θ+1)²
  1 · 3, 8 · 12, 68, 54 · 60, 532, 882, 384 … Σ 1, 11, 134, 1858, 29173, 513451, …
  (−∞, 0]nonnegative
• A114656 → basis A013610 → reverse
  1 · 3, 3 · 9, 24, 11 · 27, 135, 153, 45 … Σ 1, 6, 44, 360, 3152, 28896, 273856, …
  (−∞, 0]nonnegative
• A177267: Triangle read by rows: T(n,k) is the number of permutations of {1,2,...,n} having genus k (see first comment for definition of genus).
  5, 1 · 14, 10 · 42, 70, 8 · 132, 420, 168 … Σ 6, 24, 120, 720, 5040, 40320, 362880, …
  (−∞, 0)nonnegative
• A113953 → basis A013609 → D+1
  1 · 3, 2 · 11, 16, 4 · 27, 78, 52, 8 … Σ 1, 5, 31, 165, 867, 4401, 21951, …
  (−∞, 0]nonnegative
• A088617 → basis A007318
  1 · 2, 1 · 6, 7, 2 · 22, 41, 25, 5 … Σ 1, 3, 15, 93, 645, 4791, 37275, 299865, …
  (−∞, −1]nonnegative
• A245962 → D+1
  1 · 1 · 5, 2 · 7, 3 … Σ 1, 1, 7, 10, 29, 56, 131, 274, …
  (−∞, 0]nonnegative
• A116414 → reverse → θ+1
  1 · 1, 8 · 1, 16, 39 · 1, 24, 126, 160 … Σ 1, 9, 56, 311, 1635, 8308, 41221, …
  (−∞, 0]nonnegative
• A135065 → basis A013610
  1 · 8, 12 · 36, 108, 81 · 128, 576, 864, 432 … Σ 1, 20, 225, 2000, 15625, 112500, …
  (−∞, 0]nonnegativerational roots
• reversed rows → θ+1
  1 · 1, 4 · 1, 6 · 1, 8, 6 … Σ 1, 5, 7, 15, 26, 48, 85, 151, …
  (−∞, 0]nonnegative
• A093561 → basis A007318
  1 · 5, 1 · 10, 7, 1 · 20, 24, 9, 1 … Σ 1, 6, 18, 54, 162, 486, 1458, 4374, …
  (−∞, 0]nonnegativerational roots
• A144442 → θ+1
  1 · 1, 2 · 1, 34, 3 · 1, 236, 354, 4 … Σ 1, 3, 38, 595, 12423, 323022, 10050356, …
  (−∞, 0]nonnegative
• narayana → D → (θ+1)²
  1 · 3, 8 · 6, 48, 27 · 10, 160, 270, 64 … Σ 0, 1, 11, 81, 504, 2850, 15147, 77077, …
  (−∞, 0]nonnegative
• A114656 → basis A013611
  1 · 3, 4 · 11, 32, 16 · 45, 204, 240, 64 … Σ 1, 7, 59, 553, 5541, 58107, 629799, …
  (−∞, 0]nonnegative
• A123097 → basis A013609
  1 · 5, 4 · 14, 26, 12 · 36, 104, 100, 32 … Σ 1, 9, 52, 272, 1344, 6400, 29696, …
  (−∞, 0]nonnegativerational roots
• A093375 → D+1
  1 · 3, 1 · 7, 6, 1 · 13, 21, 9, 1 … Σ 1, 4, 14, 44, 128, 352, 928, 2368, …
  (−∞, 0]nonnegative
• A099093 → D
  3 · 3, 18 · 0, 36, 81 · 0, 18, 243, 324 … Σ 0, 3, 21, 117, 585, 2754, 12474, 54999, …
  (−∞, 0]nonnegative