Sequences

• A128813 → basis A013609
  1 · 2, 2 · 8, 20, 12 · 56, 236, 324, 144 … Σ 1, 4, 40, 760, 23560, 1083760, …
  (−∞, 0]nonnegativerational roots
• A112486 → Pₙ + Pₙ₊₁
  2, 1 · 3, 6, 3 · 8, 31, 38, 15 … Σ 3, 12, 92, 1020, 14716, 260988, …
  (−∞, ∞)nonnegative
• A165253 → (θ+1)²
  1 · 1 · 1, 4 · 1, 12, 9 … Σ 1, 1, 5, 22, 86, 313, 1085, 3629, …
  (−∞, 0]nonnegative
• A347823 → D
  3 · 8, 10 · 15, 36, 21 · 24, 84, 96, 36 … Σ 0, 3, 18, 72, 240, 720, 2016, 5376, …
  (−∞, 0]nonnegativerational roots
• A198954: Expansion of the rotational partition function for a heteronuclear diatomic molecule.
  1 · 3 · 5 · 7 … Σ 1, 3, 5, 7, 9, 11, 13, 15, …
  (−∞, −1][−1, 0]nonnegative+1
• A059364 → basis A013610
  1 · 3, 3 · 15, 33, 18 · 105, 366, 423, 162 … Σ 1, 6, 66, 1056, 22176, 576576, …
  (−∞, 0]nonnegativerational roots
• A143494 → θ+1
  1 · 2, 2 · 4, 10, 3 · 8, 38, 27, 4 … Σ 1, 4, 17, 77, 372, 1915, 10481, 60814, …
  (−∞, 0]nonnegative
• A099097 → basis A013609
  1 · 3, 6 · 10, 38, 36 · 33, 186, 348, 216 … Σ 1, 9, 84, 783, 7299, 68040, 634257, …
  (−∞, 0]nonnegative
• A109447: Binomial coefficients C(n,k) with n-k odd, read by rows.
  Veronese parent of A109447 → Veronese 2 (j=1)
  1 · 2 · 1, 3 · 4, 4 … Σ 1, 2, 4, 8, 16, 32, 64, 128, …
  (−∞, 0]nonnegative
• A038291 → basis A013609
  1 · 10, 2 · 100, 40, 4 · 1000, 600, 120, 8 … Σ 1, 12, 144, 1728, 20736, 248832, …
  (−∞, 0]nonnegativerational roots
• A125662 → basis A008277
  1 · 4, 1 · 15, 9, 1 · 56, 59, 15, 1 … Σ 1, 5, 25, 131, 722, 4187, 25531, …
  (−∞, 0]nonnegative
• A038336 → basis A013611
  484, 1760, 1600 · 10648, 58080, 105600, 64000 … Σ 3844, 238328, 14776336, 916132832, …
  (−∞, 0]nonnegativerational roots
• A081582 → Veronese 2 (j=1)
  1 · 9 · 17, 1 · 25, 25 … Σ 0, 1, 9, 18, 50, 275, 1243, 4068, …
  (−∞, 0]nonnegative
• A249248 → basis A013611
  1 · 4, 12 · 11, 52, 48 · 38, 260, 496, 192 … Σ 1, 16, 111, 986, 8691, 81726, 794541, …
  (−∞, 0]nonnegative
• A142963: Triangle read by rows, coefficients of the polynomials P(k, x) = (1/2) Sum_{p=0..k-1} Stirling2(k, p+1)*x^p*(1-4*x)^(k-1-p)*(2*p+2)!/(p+1)!.
  1 · 1, 2 · 1, 10, 4 · 1, 30, 72, 8 … Σ 1, 3, 15, 111, 1071, 12663, 177255, …
  (−∞, 0)nonnegative
• A013610 → Veronese 2
  1 · 1 · 1, 9 · 1, 27 … Σ 1, 1, 10, 28, 136, 496, 2080, 8128, …
  (−∞, 0]nonnegative
• A116412 → θ+1
  1 · 3, 2 · 6, 12, 3 · 12, 42, 27, 4 … Σ 1, 5, 21, 85, 332, 1266, 4741, 17507, …
  (−∞, 0]nonnegative
• A136124 → basis A007318
  1 · 3, 1 · 12, 7, 1 · 60, 47, 12, 1 … Σ 1, 4, 20, 120, 840, 6720, 60480, …
  (−∞, 0]nonnegativerational roots
• A391045 → (θ+1)²
  1 · 1, 4 · 1, 16, 9 · 1, 36, 90, 16 … Σ 1, 5, 26, 143, 788, 4332, 23735, …
  (−∞, 0]nonnegative
• A102547 → reverse → x ↦ x+1
  1, 1 · 1, 2, 1 · 1, 3, 3, 1 · 2, 7, 9, 5, 1 … Σ 2, 4, 8, 24, 64, 160, 416, 1088, …
  (−∞, −1]nonnegative
• A347823 → D+1
  1 · 5, 3 · 11, 18, 5 · 19, 51, 39, 7 … Σ 1, 8, 34, 116, 352, 992, 2656, 6848, …
  (−∞, 0]nonnegative
• A104684 → basis A013611
  1 · 3, 4 · 13, 32, 16 · 63, 228, 240, 64 … Σ 1, 7, 61, 595, 6145, 65527, 712909, …
  (−∞, 0]nonnegative
• A060920 → x ↦ x+1
  1 · 3, 1 · 11, 7, 1 · 43, 41, 12, 1 … Σ 1, 4, 19, 97, 508, 2683, 14209, 75316, …
  (−∞, ∞)nonnegative
• A131436: Triangle read by rows, (n-1) zeros followed by 2^n - 1.
  1 · 0, 3 · 0, 0, 7 · 0, 0, 0, 15 … Σ 1, 3, 7, 15, 31, 63, 127, 255, …
  (−∞, 0]nonnegativerational roots
• A225469 → Pₙ + Pₙ₊₁
  4, 1 · 12, 11, 1 · 36, 89, 22, 1 … Σ 5, 24, 148, 1136, 10288, 105984, …
  (−∞, ∞)nonnegative
• A376827: T(n, k) = binomial(n, k)*hypergeom([(1 - n)/2, -n/2], [1], 4).
  1 · 1, 1 · 3, 6, 3 · 7, 21, 21, 7 … Σ 1, 2, 12, 56, 304, 1632, 9024, 50304, …
  (−∞, 0)nonnegativerational roots
• A035607 → reverse
  1 · 2, 1 · 2, 4, 1 · 2, 8, 6, 1 … Σ 1, 3, 7, 17, 41, 99, 239, 577, …
  (−∞, 0]nonnegative
• A038321 → basis A013610
  324, 756, 441 · 5832, 20412, 23814, 9261 … Σ 1521, 59319, 2313441, 90224199, …
  (−∞, 0]nonnegativerational roots
• A135065 → x ↦ x+1
  1 · 8, 4 · 36, 36, 9 · 128, 192, 96, 16 … Σ 1, 12, 81, 432, 2025, 8748, 35721, …
  (−∞, −1]nonnegativerational roots
• A013610 → basis A013611
  1 · 4, 12 · 16, 96, 144 · 64, 576, 1728, 1728 … Σ 1, 16, 256, 4096, 65536, 1048576, …
  (−∞, 0]nonnegativerational roots
• A093375 → x ↦ x/(x+1)
  1 · 2, 3 · 3, 10, 8 · 4, 21, 36, 20 … Σ 1, 5, 21, 81, 297, 1053, 3645, 12393, …
  [−1, 0]nonnegativerational roots
• A008459 → D+1
  1 · 2, 1 · 5, 6, 1 · 10, 27, 12, 1 … Σ 1, 3, 12, 50, 210, 882, 3696, 15444, …
  (−∞, 0]nonnegative
• A051379 → Pₙ + Pₙ₊₁
  -7, 1 · 64, -16, 1 · -648, 225, -26, 1 … Σ -6, 49, -448, 4536, -50400, 609840, …
  (−∞, ∞)rational roots
• A116414: Riordan array (1/((1-x)(1-3x)),x/((1-x)(1-3x))).
  1 · 4, 1 · 13, 8, 1 · 40, 42, 12, 1 … Σ 1, 5, 22, 95, 409, 1760, 7573, 32585, …
  (−8, 0)nonnegative
• A038325 → basis A008277
  1 · 22, 11 · 484, 605, 121 … Σ 1, 33, 1210, 49247, 2210791, 108548374, …
  (−∞, 0]nonnegative
• A257627: Triangle, read by rows, T(n,k) = t(n-k, k) where t(n,m) = f(m)*t(n-1,m) + f(n)*t(n,m-1) and f(x) = 7*x + 3.
  1 · 3, 3 · 9, 60, 9 · 27, 753, 753, 27 … Σ 1, 6, 78, 1560, 42120, 1432080, …
  (−∞, 0)nonnegative
• A154986 → basis A008277
  1 · 2, 1 · 6, 7, 1 · 24, 51, 17, 1 … Σ 1, 3, 14, 93, 811, 8914, 118881, …
  (−∞, 0]nonnegative
• A103406 → D
  2 · 4, 6 · 6, 18, 12 · 8, 36, 48, 20 … Σ 0, 2, 10, 36, 112, 320, 864, 2240, …
  (−∞, 0]nonnegativerational roots
• A038333 → basis A013609
  361, 532, 196 · 6859, 15162, 11172, 2744 … Σ 1089, 35937, 1185921, 39135393, …
  (−∞, 0]nonnegativerational roots
• A038334 → basis A007318
  400, 320, 64 · 8000, 9600, 3840, 512 … Σ 784, 21952, 614656, 17210368, …
  (−∞, 0]nonnegativerational roots
• basis-map coefficients of A297191, shifted → basis A008277
  1 · 1, 3, 1 · 1, 15, 25, 10, 1 … Σ 1, 5, 52, 877, 21147, 678570, 27644437, …
  (−∞, 0]nonnegative
• A327997 → basis A013609
  1 · 4, 2 · 17, 18, 4 · 78, 130, 60, 8 … Σ 1, 6, 39, 276, 2133, 18018, 166203, …
  (−∞, 0]nonnegative
• A125662 → x ↦ x/(x+1)
  1 · 3, 4 · 8, 22, 15 · 21, 88, 122, 56 … Σ 1, 7, 45, 287, 1829, 11655, 74269, …
  [−1, −1/2)nonnegative
• A143494 → D
  1 · 5, 2 · 19, 18, 3 · 65, 110, 42, 4 … Σ 0, 1, 7, 40, 221, 1241, 7218, 43807, …
  (−∞, 0]nonnegative
• basis-map coefficients of A145596 → D
  2 · 2, 6 · -8, 16, 12 · -10, -30, 60, 20 … Σ 0, 2, 8, 20, 40, 70, 112, 168, …
  (−∞, ∞)
• Stirling2 triangle with scaled diagonals (powers of 10).
  100, 30, 1 · 1000, 700, 60, 1 … Σ 131, 1761, 27601, 506651, 10674211, …
  (−∞, 0)nonnegative
• A358735 → basis A013610
  1 · 2, 3 · 7, 24, 18 · 33, 180, 306, 162 … Σ 1, 5, 49, 681, 12209, 267917, 6953633, …
  (−∞, 0]nonnegative
• A028326 → basis A013609
  2 · 4, 4 · 8, 16, 8 · 16, 48, 48, 16 … Σ 2, 8, 32, 128, 512, 2048, 8192, 32768, …
  (−∞, 0]nonnegativerational roots
• A094638 → basis A013609
  1 · 2, 2 · 6, 14, 8 · 24, 92, 116, 48 … Σ 1, 4, 28, 280, 3640, 58240, 1106560, …
  (−∞, 0]nonnegativerational roots
• A204420 → basis A013611
  1 · 1, 4 · 9, 48, 48 · 225, 1380, 2160, 960 … Σ 1, 5, 105, 4725, 363825, 42567525, …
  (−∞, 0]nonnegativerational roots