Sequences

• A026374: Triangular array T read by rows: T(n,0) = T(n,n) = 1 for all n >= 0, T(n,k) = T(n-1,k-1) + T(n-1,k) for odd n and 1< = k <= n-1, T(n,k) = T(n-1,k-1) +…
  1 · 1, 1 · 1, 3, 1 · 1, 4, 4, 1 … Σ 1, 2, 5, 10, 25, 50, 125, 250, …
  (−∞, 0]nonnegative
• A038207 → Veronese 2 (j=1)
  1 · 4 · 12, 1 · 32, 8 … Σ 0, 1, 4, 13, 40, 121, 364, 1093, …
  (−∞, 0]nonnegative
• A091042 → D+1
  1 · 4, 3 · 11, 20, 5 · 22, 91, 56, 7 … Σ 1, 7, 36, 176, 832, 3840, 17408, 77824, …
  (−∞, 0]nonnegative
• A081577 → Veronese 2
  1 · 1 · 1, 1 · 1, 7 … Σ 1, 1, 2, 8, 24, 60, 160, 448, …
  (−∞, 0]nonnegative
• A188440 → basis A007318
  1 · 1 · 3, 2 · 3, 2 … Σ 1, 1, 5, 5, 25, 25, 125, 125, …
  (−∞, −1]nonnegativerational roots
• A367270 → D
  2 · 6, 6 · 12, 36, 12 · 20, 120, 120, 20 … Σ 0, 0, 2, 12, 60, 280, 1260, 5544, …
  (−∞, 0]nonnegative
• A099093 → x ↦ x−3
  1 · -9, 3 · 72, -51, 9 · -567, 621, -225, 27 … Σ 1, -6, 30, -144, 684, -3240, 15336, …
  (5/3, 3]
• A120910 → θ+1
  3 · 6, 6 · 12, 24, 9 · 24, 72, 54, 12 … Σ 3, 12, 45, 162, 567, 1944, 6561, 21870, …
  (−∞, 0]nonnegativerational roots
• A128100 → basis A008277
  1 · 1 · 3, 1 · 5, 2 … Σ 1, 1, 4, 7, 20, 43, 113, 267, …
  (−∞, 0]nonnegative
• A106800: Triangle of Stirling numbers of 2nd kind, S(n, n-k), n >= 0, 0 <= k <= n.
  1 · 1 · 1, 1 · 1, 3, 1 … Σ 1, 1, 2, 5, 15, 52, 203, 877, …
  (−∞, 0)nonnegative
• A048176 → Pₙ + Pₙ₊₁
  -9, 1 · 190, -29, 1 · -5800, 1070, -59, 1 … Σ -8, 162, -4788, 188442, -9283248, …
  (−∞, ∞)rational roots
• A241171: Triangle read by rows: Joffe's central differences of zero, T(n,k), 1 <= k <= n.
  1 · 1, 6 · 1, 30, 90 · 1, 126, 1260, 2520 … Σ 1, 7, 121, 3907, 202741, 15430207, …
  (−∞, 0]nonnegative
• A038329 → basis A013609
  225, 180, 36 · 3375, 4050, 1620, 216 … Σ 441, 9261, 194481, 4084101, 85766121, …
  (−∞, 0]nonnegativerational roots
• A207823 → basis A013609
  1 · 5, 2 · 24, 20, 4 · 115, 146, 60, 8 … Σ 1, 7, 48, 329, 2255, 15456, 105937, …
  (−∞, 0]nonnegative
• A113214 → x ↦ x−4
  1 · -2, 1 · 4, -5, 1 · -8, 18, -8, 1 … Σ 1, -1, 0, 3, -9, 18, -27, 27, …
  (0, 4]
• A038208 → basis A013610
  1 · 4, 6 · 16, 48, 36 · 64, 288, 432, 216 … Σ 1, 10, 100, 1000, 10000, 100000, …
  (−∞, 0]nonnegativerational roots
• A207823 → θ+1
  1 · 4, 2 · 15, 16, 3 · 56, 92, 36, 4 … Σ 1, 6, 34, 188, 1021, 5468, 28959, …
  (−∞, 0]nonnegative
• A038271 → basis A013609
  1 · 12, 10 · 144, 240, 100 · 1728, 4320, 3600, 1000 … Σ 1, 22, 484, 10648, 234256, 5153632, …
  (−∞, 0]nonnegativerational roots
• A028338: Triangle of coefficients in expansion of (x+1)*(x+3)*...*(x + 2n - 1) in rising powers of x.
  1 · 1, 1 · 3, 4, 1 · 15, 23, 9, 1 … Σ 1, 2, 8, 48, 384, 3840, 46080, 645120, …
  (−∞, 0)nonnegativerational roots
• A081581 → basis A008277
  1 · 2, 1 · 10, 11, 1 · 32, 67, 21, 1 … Σ 1, 3, 22, 121, 817, 5570, 40985, …
  (−∞, 0]nonnegative
• A008292 → θ+1
  1 · 1, 2 · 1, 8, 3 · 1, 22, 33, 4 … Σ 0, 1, 3, 12, 60, 360, 2520, 20160, …
  (−∞, 0]nonnegative
• A081580 → basis A007318
  1 · 2, 1 · 9, 9, 1 · 28, 42, 16, 1 … Σ 1, 3, 19, 87, 451, 2223, 11179, 55767, …
  (−∞, −1]nonnegative
• A075503 → Pₙ + Pₙ₊₁
  576, 472, 49, 1 · 4608, 8128, 1648, 81, 1 … Σ 1098, 14466, 223562, 3957858, 78313226, …
  (−∞, ∞)nonnegative
• Matrix product of Stirling2-triangle A008277(n,k) and unsigned Lah-triangle |A008297(n,k)|.
  13, 9, 1 · 75, 79, 18, 1 · 541, 765, 265, 30, 1 … Σ 23, 173, 1602, 17575, 222497, 3188806, …
  (−∞, 0]nonnegative
• A028326 → D+1
  2 · 4, 2 · 6, 8, 2 · 8, 18, 12, 2 … Σ 2, 6, 16, 40, 96, 224, 512, 1152, …
  (−∞, 0]nonnegativerational roots
• A052553 → θ+1
  1 · 1 · 1, 2 · 1, 4 … Σ 1, 1, 3, 5, 10, 18, 33, 59, …
  (−∞, 0]nonnegative
• A063967 → x ↦ x−2
  1 · -1, 1 · 0, -1, 1 · 1, -1, -1, 1 … Σ 1, 0, 0, 0, 0, 0, 0, 0, …
  (−3, 1]
• A055356: Triangle of increasing mobiles (circular rooted trees) with n nodes and k leaves.
  1 · 1 · 1, 1 · 1, 4, 2 … Σ 1, 1, 2, 7, 36, 245, 2076, 21059, …
  (−∞, 0)nonnegative
• A207823 → x ↦ x/(x+1)
  1 · 4, 5 · 15, 38, 24 · 56, 214, 272, 115 … Σ 1, 9, 77, 657, 5605, 47817, 407933, …
  [−1, −2/3)nonnegative
• A266213 → (θ+1)²
  1 · 1 · 1, 8 · 1, 16, 18 … Σ 1, 1, 9, 35, 129, 437, 1409, 4375, …
  (−∞, 0]nonnegative
• A091042 → basis A013609
  1 · 4, 6 · 16, 40, 20 · 64, 224, 224, 56 … Σ 1, 10, 76, 568, 4240, 31648, 236224, …
  (−∞, 0]nonnegative
• A038335 → basis A013610
  1 · 21, 27 · 441, 1134, 729 … Σ 1, 48, 2304, 110592, 5308416, …
  (−∞, 0]nonnegativerational roots
• A130534 → x ↦ x/(x+1)
  1 · 1, 2 · 2, 7, 6 · 6, 29, 46, 24 … Σ 1, 3, 15, 105, 945, 10395, 135135, …
  [−1, 0]nonnegativerational roots
• A114656 → basis A008277
  1 · 3, 1 · 11, 9, 1 · 45, 67, 18, 1 … Σ 1, 4, 21, 131, 928, 7275, 62051, …
  (−∞, 0]nonnegative
• A038231 → x ↦ x/(x+1)
  1 · 4, 5 · 16, 40, 25 · 64, 240, 300, 125 … Σ 1, 9, 81, 729, 6561, 59049, 531441, …
  [−1, 0]nonnegativerational roots
• A064861 → x ↦ x/(x+1)
  1, 5, 6 · 1, 8, 21, 18 · 1, 10, 37, 60, 36 … Σ 12, 48, 144, 576, 1728, 6912, 20736, …
  [−1, 0]nonnegativerational roots
• A156992 → basis A008277
  1 · 4, 2 · 24, 30, 6 · 192, 456, 216, 24 … Σ 1, 6, 60, 888, 18120, 485280, 16445520, …
  (−∞, 0]nonnegative
• A178821 → basis A013609
  1 · 10, 10 · 60, 120, 60 · 280, 840, 840, 280 … Σ 1, 20, 240, 2240, 17920, 129024, …
  (−∞, 0]nonnegativerational roots
• A274496 → D
  2 · 4 · 8, 8 · 16, 16 … Σ 0, 0, 2, 4, 16, 32, 96, 192, …
  (−∞, 0]nonnegativerational roots
• A023531 → x ↦ x−1
  1 · -1, 1 · 1, -2, 1 · -1, 3, -3, 1 … Σ 1, 0, 0, 0, 0, 0, 0, 0, …
  (−∞, 1][0, ∞)rational roots
• A113214 → Veronese 2
  1 · 2 · 0, 1 · 0, 4 … Σ 1, 2, 1, 4, 6, 8, 15, 24, …
  (−∞, 0]nonnegative
• A063967 → x ↦ x−7
  1 · -6, 1 · 30, -11, 1 · -144, 84, -16, 1 … Σ 1, -5, 20, -75, 275, -1000, 3625, …
  (2, 6]
• A249251 → Veronese 2 (j=1)
  3 · 6 · 9, 12 · 12, 60 … Σ 0, 3, 6, 21, 72, 234, 774, 2559, …
  (−∞, 0]nonnegative
• A131431 → θ+1
  1 · 0, 8 · 0, 0, 21 · 0, 0, 0, 40 … Σ 1, 8, 21, 40, 65, 96, 133, 176, …
  (−∞, 0]nonnegativerational roots
• A127773: Triangle read by rows: row n consists of n-1 zeros followed by n(n+1)/2.
  1 · 0, 3 · 0, 0, 6 · 0, 0, 0, 10 … Σ 1, 3, 6, 10, 15, 21, 28, 36, …
  [−1, 0]nonnegativerational roots
• A131431 → (θ+1)²
  1 · 0, 16 · 0, 0, 63 · 0, 0, 0, 160 … Σ 1, 16, 63, 160, 325, 576, 931, 1408, …
  (−∞, 0]nonnegativerational roots
• A118424: Triangle read by rows: T(n,k) is the number of binary sequences of length n containing k subsequences 001 (n,k>=0).
  A102547 → x ↦ (1/8)x−1/8
  1 · 2 · 4 · 7, 1 … Σ 1, 2, 4, 8, 16, 32, 64, 128, …
  (−∞, 1]nonnegative
• A144438 → D
  1 · 5, 2 · 14, 28, 3 · 33, 178, 99, 4 … Σ 0, 1, 7, 45, 314, 2430, 20883, 198310, …
  (−∞, 0]nonnegative
• A110441 → Veronese 2 (j=1)
  1 · 6 · 23, 1 · 72, 12 … Σ 0, 1, 6, 24, 84, 284, 960, 3264, …
  (−∞, 0]nonnegative
• A290319 → basis A013610
  1 · 2, 3 · 12, 24, 9 · 120, 276, 162, 27 … Σ 1, 5, 45, 585, 9945, 208845, 5221125, …
  (−∞, 0]nonnegativerational roots