Sequences

• A111125 → basis A007318 → θ+1
  1 · 4, 2 · 11, 14, 3 · 29, 62, 30, 4 … Σ 1, 6, 28, 125, 543, 2312, 9694, 40155, …
  (−∞, 0]nonnegative
• A227450 → x ↦ x/(x+1)
  2 · 2, 6 · 2, 16, 22 · 2, 34, 110, 94 … Σ 2, 8, 40, 240, 1664, 12992, 112256, …
  [−1, 0]nonnegative
• A038322 → basis A013610 → D
  24 · 912, 1152 · 25992, 65664, 41472 … Σ 0, 24, 2064, 133128, 7632672, …
  (−∞, 0]nonnegativerational roots
• A094638 → basis A013611 → (θ+1)²
  1 · 2, 16 · 6, 112, 288 · 24, 736, 4176, 6144 … Σ 1, 18, 406, 11080, 355816, 13159376, …
  (−∞, 0]nonnegative
• A099097 → basis A007318 → basis A013611
  1 · 6, 12 · 38, 148, 144 · 240, 1392, 2688, 1728 … Σ 1, 18, 330, 6048, 110844, 2031480, …
  (−∞, 0]nonnegative
• A069466 → γ → (θ+1)²
  1 · 2 · 6, 48 · 20, 480 … Σ 1, 2, 54, 500, 7210, 88452, 1155924, …
  (−∞, 0]nonnegative
• A347056 → D
  4 · 16, 20 · 40, 100, 60 · 80, 300, 360, 140 … Σ 0, 4, 36, 200, 880, 3360, 11648, 37632, …
  (−∞, 0]nonnegativerational roots
• A059473 → basis A013609 → reverse
  1 · 4, 4 · 16, 36, 18 · 64, 224, 240, 80 … Σ 1, 8, 70, 608, 5284, 45920, 399064, …
  (−∞, 0]nonnegative
• A122542 → x ↦ x+1 → basis A008277
  1 · 2, 1 · 8, 7, 1 · 28, 41, 13, 1 … Σ 1, 3, 16, 83, 459, 2674, 16407, 105799, …
  (−∞, 0]nonnegative
• A142459 → (θ+1)²
  1 · 1, 4 · 1, 40, 9 · 1, 236, 531, 16 … Σ 1, 5, 50, 784, 15744, 384240, 11004000, …
  (−∞, 0]nonnegative
• A118933 → basis A013610 → x ↦ x+1
  1 · 1 · 1 · 1 … Σ 1, 1, 1, 1, 43, 211, 631, 1471, …
  (−∞, −1]nonnegative
• A178821 → basis A013611 → basis A013610
  1 · 30, 60 · 540, 2160, 2160 … Σ 1, 90, 4860, 204120, 7348320, …
  (−∞, 0]nonnegativerational roots
• A013620 → basis A008288 → basis A013609
  1 · 8, 6 · 73, 114, 36 · 674, 1584, 1080, 216 … Σ 1, 14, 223, 3554, 56641, 902702, …
  (−∞, 0]nonnegative
• A172431 → (θ+1)²
  1 · 1, 8 · 1, 16, 27 · 1, 24, 90, 64 … Σ 1, 9, 44, 179, 667, 2352, 7973, 26229, …
  (−∞, 0]nonnegative
• A052553 → D → (θ+1)²
  1 · 2 · 3, 8 · 4, 24 … Σ 0, 0, 1, 2, 11, 28, 80, 194, …
  (−∞, 0]nonnegative
• A030528 → x ↦ x−1
  1 · 0, 1 · -1, 0, 1 · 1, -2, 0, 1 … Σ 1, 1, 0, 0, 0, 0, 0, 0, …
  (−3, 1]
• A038323 → basis A013610 → reverse
  1 · 27, 20 · 729, 1080, 400 … Σ 1, 47, 2209, 103823, 4879681, …
  (−∞, 0]nonnegativerational roots
• A035607 → basis A013611 → basis A013609
  1 · 1 · 11, 16 · 71, 192, 128 … Σ 1, 1, 27, 391, 5825, 86633, 1288587, …
  (−∞, 0]nonnegative
• A153648: Triangle T(n, k) = T(n-1, k) + T(n-1, k-1) + j*prime(j)*T(n-2, k-1) with j=3, read by rows.
  2 · 5, 5 · 2, 46, 2 · 2, 123, 123, 2 … Σ 2, 10, 50, 250, 1250, 6250, 31250, …
  (−∞, 0)nonnegative
• A128813 → basis A013610 → D+1
  1 · 5, 3 · 38, 84, 27 · 410, 1812, 2187, 486 … Σ 1, 8, 149, 4895, 249445, 18214270, …
  (−∞, 0]nonnegative
• A081577 → basis A013610 → basis A008277
  1 · 5, 3 · 33, 45, 9 · 205, 531, 252, 27 … Σ 1, 8, 87, 1015, 13064, 183045, 2770771, …
  (−∞, 0]nonnegative
• A115951 → D+1
  1 · 2, 2 · 2, 14, 6 · 0, 24, 72, 20 … Σ 1, 4, 22, 116, 608, 3152, 16208, 82784, …
  (−∞, 0]nonnegative
• A112493 → x ↦ x/(x+1)
  1 · 1, 2 · 1, 6, 8 · 1, 14, 50, 52 … Σ 1, 3, 15, 117, 1269, 17667, 300375, …
  [−1, 0)nonnegative
• A038243 → basis A013611 → basis A008277
  1 · 10, 4 · 100, 96, 16 · 1000, 1744, 672, 64 … Σ 1, 14, 212, 3480, 61840, 1185248, …
  (−∞, 0]nonnegative
• A131222 → θ+1
  1 · 0, 2 · 0, 6, 3 · 0, 28, 27, 4 … Σ 1, 2, 9, 59, 506, 5354, 67344, 981336, …
  (−∞, 0]nonnegative
• A272867 → D+1
  1 · 5, 6, 1 · 9, 44, 42, 12, 1 … Σ 1, 12, 108, 864, 6480, 46656, 326592, …
  (−∞, 0]nonnegative
• A249248 → reverse → basis A007318
  1 · 4, 1 · 11, 9, 1 · 38, 49, 15, 1 … Σ 1, 5, 21, 103, 519, 2793, 15645, 91623, …
  (−∞, −1]nonnegative
• A062190 → θ+1
  1 · 1, 12 · 1, 28, 63 · 1, 48, 252, 224 … Σ 1, 13, 92, 525, 2695, 13013, 60424, …
  (−∞, 0]nonnegative
• A028313 → basis A007318
  1 · 2, 1 · 7, 7, 1 · 14, 21, 9, 1 … Σ 1, 3, 15, 45, 135, 405, 1215, 3645, …
  (−∞, 0]nonnegative
• A102547 → basis A013609
  1 · 1 · 1 · 2, 2 … Σ 1, 1, 1, 4, 7, 10, 22, 43, …
  (−∞, 0]nonnegative
• A080248 → x ↦ x/(x+1)
  1 · 1, 2 · 1, 6, 6 · 1, 16, 39, 25 … Σ 1, 3, 13, 81, 669, 6955, 88505, …
  [−1, 0]nonnegative
• A013622 → basis A013609 → θ+1
  1 · 8, 20 · 64, 320, 300 · 512, 3840, 7200, 4000 … Σ 1, 28, 684, 15552, 338256, 7138368, …
  (−∞, 0]nonnegativerational roots
• A038221 → basis A013609 → D+1
  1 · 12, 6 · 108, 144, 36 · 864, 1944, 1296, 216 … Σ 1, 18, 288, 4320, 62208, 870912, …
  (−∞, 0]nonnegativerational roots
• A055151 → basis A007318 → x ↦ x+1
  1 · 1 · 3, 1 · 7, 3 … Σ 1, 1, 4, 10, 37, 121, 451, 1639, …
  (−∞, −1]nonnegative
• A116666 → Veronese 2 (j=1) → D+1
  3 · 6 · 16, 7 · 40, 28 … Σ 0, 3, 6, 23, 68, 188, 496, 1264, …
  (−∞, 0]nonnegative
• A173018 → θ+1
  1 · 1 · 1, 2 · 1, 8, 3 … Σ 1, 1, 3, 12, 60, 360, 2520, 20160, …
  (−∞, 0]nonnegative
• A056242: Triangle read by rows: T(n,k) = number of k-part order-consecutive partition of {1,2,...,n} (1 <= k <= n).
  1 · 1, 2 · 1, 5, 4 · 1, 9, 16, 8 … Σ 1, 3, 10, 34, 116, 396, 1352, 4616, …
  [−1, 0]nonnegative
• A008299 → x ↦ x+1
  1 · 1 · 4, 3 · 11, 10 … Σ 1, 1, 7, 21, 111, 533, 3039, 18245, …
  (−∞, −1]nonnegative
• A064861 → basis A013611
  6, 28, 32 · 18, 132, 320, 256 … Σ 66, 726, 4356, 47916, 287496, 3162456, …
  (−∞, 0]nonnegativerational roots
• A120910 → basis A013609 → basis A008277
  3 · 15, 6 · 75, 72, 12 · 375, 654, 252, 24 … Σ 3, 21, 159, 1305, 11595, 111117, …
  (−∞, 0]nonnegative
• A063007 → basis A008277
  1 · 3, 2 · 13, 24, 6 · 63, 242, 150, 20 … Σ 1, 5, 43, 475, 6231, 93427, 1564249, …
  (−∞, 0]nonnegative
• type_b_eulerian → γ (scale 1/4) → D → x ↦ x+1
  1 · 5 · 28, 10 · 180, 122 … Σ 0, 0, 1, 5, 38, 302, 2827, 29607, …
  (−∞, −1]nonnegative
• A046716 → basis A013609 → x ↦ x+1
  1 · 4, 2 · 19, 18, 4 · 118, 162, 68, 8 … Σ 1, 6, 41, 356, 4401, 78826, 1893481, …
  (−∞, −1]nonnegative
• A039756 → reverse → D
  1 · 4, 2 · 13, 18, 3 · 40, 116, 48, 4 … Σ 0, 1, 6, 34, 208, 1396, 10232, 81320, …
  (−∞, 0]nonnegative
• A207607 → basis A007318 → x ↦ x+1
  1 · 5, 2 · 19, 13, 2 · 71, 69, 21, 2 … Σ 1, 7, 34, 163, 781, 3742, 17929, 85903, …
  (−6, −2)nonnegative
• A093645: (10,1) Pascal triangle.
  1 · 10, 1 · 10, 11, 1 · 10, 21, 12, 1 … Σ 1, 11, 22, 44, 88, 176, 352, 704, …
  (−∞, 0)nonnegativerational roots
• A039756: Triangle of B-analogs of Stirling numbers of 2nd kind.
  1 · 1, 1 · 1, 4, 1 · 1, 9, 13, 1 … Σ 1, 2, 6, 24, 116, 648, 4088, 28640, …
  (−∞, 0)nonnegative
• basis-map coefficients of A030528, shifted → θ+1 → basis A013609
  1 · -2, -4 · 3, 12, 12 · -4, -24, -48, -32 … Σ 1, -6, 27, -108, 405, -1458, 5103, …
  (−∞, 0]rational roots
• A352880 → reverse → (θ+1)²
  8 · 18, 48 · 32, 256, 144 · 50, 800, 1350, 320 … Σ 8, 66, 432, 2520, 13680, 70686, 352352, …
  (−∞, 0]nonnegative
• A063007 → basis A013610 → (θ+1)²
  1 · 3, 24 · 13, 216, 486 · 63, 1584, 7290, 8640 … Σ 1, 27, 715, 17577, 409641, 9186939, …
  (−∞, 0]nonnegative