Sequences

• A128100: Triangle read by rows: T(n,k) is the number of ways to tile a 2 X n rectangle with k pieces of 2 X 2 tiles and n-2k pieces of 1 X 2 tiles (0 <= k <= f…
  1 · 1 · 2, 1 · 3, 2 … Σ 1, 1, 3, 5, 11, 21, 43, 85, …
  (−∞, −1]nonnegative
• A013613 → Pₙ + Pₙ₊₁
  2, 6 · 2, 18, 36 · 2, 30, 144, 216 … Σ 8, 56, 392, 2744, 19208, 134456, …
  (−∞, ∞)nonnegativerational roots
• A173018 → reverse (shift +1) → reverse
  1 · 1 · 1, 1 · 1, 4, 1 … Σ 1, 1, 2, 6, 24, 120, 720, 5040, …
  (−∞, 0]nonnegative
• A123519 → basis A008277
  11, 18, 4 · 41, 128, 68, 8 · 153, 832, 796, 216, 16 … Σ 33, 245, 2013, 18105, 176589, 1853433, …
  (−∞, 0]nonnegative
• A225469: Triangle read by rows, S_4(n, k) where S_m(n, k) are the Stirling-Frobenius subset numbers of order m; n >= 0, k >= 0.
  1 · 3, 1 · 9, 10, 1 · 27, 79, 21, 1 … Σ 1, 4, 20, 128, 1008, 9280, 96704, …
  (−∞, 0)nonnegative
• A007318 → ×(−(1/2)n+(1/2)n²) → D
  2, 2 · 9, 18, 9 · 24, 72, 72, 24 … Σ 0, 0, 4, 36, 192, 800, 2880, 9408, …
  (−∞, 0]nonnegativerational roots
• A176230: Exponential Riordan array [1/sqrt(1-2x), x/(1-2x)].
  1 · 1, 1 · 3, 6, 1 · 15, 45, 15, 1 … Σ 1, 2, 10, 76, 764, 9496, 140152, …
  (−∞, 0)nonnegative
• A125662 → basis A013609
  1 · 4, 2 · 15, 16, 4 · 56, 92, 48, 8 … Σ 1, 6, 35, 204, 1189, 6930, 40391, …
  (−∞, 0]nonnegative
• A132774 → x ↦ x/(x+1)
  1 · 2, 5 · 0, 4, 9 · 0, 0, 6, 13 … Σ 1, 7, 13, 19, 25, 31, 37, 43, …
  [−1, 0]nonnegativerational roots
• A166340 → γ
  1, 6 · 1, 16 · 1, 38, 32 · 1, 84, 248 … Σ 7, 17, 71, 333, 1923, 12513, 92799, …
  (−∞, 0]nonnegative
• Triangle whose (i,j)-th entry is binomial(i,j)*11^(i-j)*7^j.
  121, 154, 49 · 1331, 2541, 1617, 343 … Σ 324, 5832, 104976, 1889568, 34012224, …
  (−∞, 0)nonnegativerational roots
• A272867 → basis A013611
  1 · 6, 24, 16 · 36, 288, 768, 768, 256 … Σ 1, 46, 2116, 97336, 4477456, 205962976, …
  (−∞, 0]nonnegative
• A113214 → basis A013611
  1 · 3, 4 · 4, 20, 16 · 7, 52, 112, 64 … Σ 1, 7, 40, 235, 1375, 8050, 47125, …
  (−∞, 0]nonnegative
• A038334 → basis A013609
  400, 640, 256 · 8000, 19200, 15360, 4096 … Σ 1296, 46656, 1679616, 60466176, …
  (−∞, 0]nonnegativerational roots
• A113413 → x ↦ x/(x+1)
  1 · 2, 3 · 2, 8, 7 · 2, 14, 28, 17 … Σ 1, 5, 17, 61, 217, 773, 2753, 9805, …
  [−1, 0]nonnegative
• A075497 → reverse
  1 · 1, 2 · 1, 6, 4 · 1, 12, 28, 8 … Σ 1, 3, 11, 49, 257, 1539, 10299, 75905, …
  (−∞, 0]nonnegative
• A299989: Triangle read by rows: T(n,0) = 0 for n >= 0; T(n,2*k+1) = A152842(2*n,2*(n-k)) and T(n,2*k) = A152842(2*n,2*(n-k)+1) for n >= k > 0.
  0, 1 · 0, 3, 4, 1 · 0, 9, 24, 22, 8, 1 … Σ 1, 8, 64, 512, 4096, 32768, 262144, …
  (−∞, 0]nonnegativerational roots
• A038305 → basis A013610
  169, 234, 81 · 2197, 4563, 3159, 729 … Σ 484, 10648, 234256, 5153632, 113379904, …
  (−∞, 0]nonnegativerational roots
• A144698: Triangle of 4-Eulerian numbers.
  1 · 1, 4 · 1, 13, 16 · 1, 32, 113, 64 … Σ 1, 5, 30, 210, 1680, 15120, 151200, …
  (−∞, 0)nonnegative
• A225117 → Pₙ + Pₙ₊₁
  3, 1 · 6, 14, 1 · 12, 106, 61, 1 … Σ 4, 21, 180, 2106, 31104, 554040, …
  (−∞, ∞)nonnegative
• A038220 → Veronese 2 (j=1)
  2 · 12 · 54, 8 · 216, 96 … Σ 0, 2, 12, 62, 312, 1562, 7812, 39062, …
  (−∞, 0]nonnegative
• A039756 → x ↦ x/(x+1)
  1 · 1, 2 · 1, 6, 6 · 1, 12, 34, 24 … Σ 1, 3, 13, 71, 457, 3355, 27509, 248127, …
  [−1, 0]nonnegative
• A038338 → Pₙ + Pₙ₊₁
  1872, 5472, 5328, 1728 … Σ 14400, 345600, 8294400, 199065600, …
  (−∞, ∞)nonnegativerational roots
• A075497 → x ↦ x+1
  1 · 3, 1 · 11, 8, 1 · 49, 55, 15, 1 … Σ 1, 4, 20, 120, 832, 6496, 56128, …
  (−∞, −1]nonnegative
• A130123 → (θ+1)²
  1 · 0, 8 · 0, 0, 36 · 0, 0, 0, 128 … Σ 1, 8, 36, 128, 400, 1152, 3136, 8192, …
  (−∞, 0]nonnegativerational roots
• A038243 → basis A013610
  1 · 6, 3 · 36, 36, 9 · 216, 324, 162, 27 … Σ 1, 9, 81, 729, 6561, 59049, 531441, …
  (−∞, 0]nonnegativerational roots
• A225473 → Pₙ + Pₙ₊₁
  4, 4 · 12, 44, 32 · 36, 356, 704, 384 … Σ 8, 88, 1480, 33688, 963976, 33191128, …
  (−∞, ∞)nonnegative
• A094305: Triangle read by rows: T(n,k) = ((n+1)(n+2)/2) * binomial(n,k) (0 <= k <= n).
  1 · 3, 3 · 6, 12, 6 · 10, 30, 30, 10 … Σ 1, 6, 24, 80, 240, 672, 1792, 4608, …
  (−∞, −1]nonnegativerational roots
• A026729 → basis A013610
  1 · 1, 3 · 2, 9, 9 · 3, 21, 45, 27 … Σ 1, 4, 20, 96, 464, 2240, 10816, 52224, …
  (−∞, 0]nonnegative
• A114655 → D+1
  2 · 6, 2 · 20, 16, 2 · 64, 96, 30, 2 … Σ 2, 8, 38, 192, 1002, 5336, 28814, …
  (−∞, 0]nonnegative
• A114655 → θ+1
  2 · 4, 4 · 8, 24, 6 · 16, 96, 72, 8 … Σ 2, 8, 38, 192, 1002, 5336, 28814, …
  (−∞, 0]nonnegative
• A056939 → γ
  1 · 1 · 1, 2 · 1, 7 … Σ 1, 1, 3, 8, 29, 106, 436, 1849, …
  (−∞, 0]nonnegative
• A134059: Triangle T(n, k) = 3*binomial(n,k) with T(0, 0) = 1, read by rows.
  1 · 3, 3 · 3, 6, 3 · 3, 9, 9, 3 … Σ 1, 6, 12, 24, 48, 96, 192, 384, …
  (−∞, 0)nonnegativerational roots
• A178820 → Veronese 2
  1 · 4 · 10, 10 · 20, 60 … Σ 1, 4, 20, 80, 280, 896, 2688, 7680, …
  (−∞, 0]nonnegative
• A085841 → basis A008277
  1 · 7, 4 · 61, 88, 16 · 547, 1596, 720, 64 … Σ 1, 11, 165, 2927, 58633, 1295123, …
  (−∞, 0]nonnegative
• A118931 → basis A008277
  1 · 1 · 1 · 3, 2 … Σ 1, 1, 1, 5, 17, 41, 281, 1541, …
  (−∞, 0]nonnegative
• A099097 → x ↦ x−12
  1 · -36, 3 · 1284, -215, 9 · -45792, 11520, -966, 27 … Σ 1, -33, 1078, -35211, 1150105, …
  (104/9, 12]
• A249250 → basis A013610
  1 · 4, 9 · 10, 36, 27 · 28, 144, 216, 81 … Σ 1, 13, 73, 469, 2929, 18397, 115417, …
  (−∞, 0]nonnegative
• A122431 → x ↦ x/(x+1)
  1, 6, 12, 8 · 0, 1, 6, 12, 8 · 0, 0, 1, 6, 12, 8 … Σ 27, 27, 27, 27, 27, 27, 27, 27, …
  [−1, 0]nonnegativerational roots
• A152842 → D+1
  1 · 4, 3 · 5, 10, 3 · 8, 37, 42, 9 … Σ 1, 7, 18, 96, 224, 1088, 2432, 11264, …
  (−∞, 0]nonnegative
• A059364: Triangle T(n,k)=Sum_{i=0..n} |stirling1(n,n-i)|*binomial(i,k), k=0..n-1.
  1 · 2, 1 · 6, 7, 2 · 24, 46, 29, 6 … Σ 1, 3, 15, 105, 945, 10395, 135135, …
  (−∞, −1]nonnegativerational roots
• A290316: Triangle T(n, k) read by rows: row n gives the coefficients of the numerator polynomials of the o.g.f. of the (n+1)-th diagonal of the Sheffer triangl…
  1 · 1, 6 · 1, 48, 90 · 1, 234, 2214, 2160 … Σ 1, 7, 139, 4609, 214297, 12820999, …
  (−∞, 0)nonnegative
• A086645 → basis A013611
  1 · 2, 4 · 8, 32, 16 · 32, 192, 288, 64 … Σ 1, 6, 56, 576, 6016, 62976, 659456, …
  (−∞, 0]nonnegative
• A059344 → D
  2 · 6 · 12, 24 · 20, 120 … Σ 0, 0, 2, 6, 36, 140, 750, 3402, …
  (−∞, 0]nonnegative
• A103406: Triangle read by rows: n-th row = unsigned coefficients of the characteristic polynomials of an n X n matrix with 2's on the diagonal and 1's elsewher…
  1 · 1, 2 · 1, 4, 3 · 1, 6, 9, 4 … Σ 1, 3, 8, 20, 48, 112, 256, 576, …
  (−∞, 0)nonnegativerational roots
• A035607 → basis A008277
  1 · 1 · 3, 2 · 7, 10, 2 … Σ 1, 1, 5, 19, 83, 391, 1989, 10841, …
  (−∞, 0]nonnegative
• A249252 → (θ+1)²
  1 · 1, 16 · 1, 32, 72 · 1, 48, 288, 256 … Σ 1, 17, 105, 593, 3049, 14801, 68873, …
  (−∞, 0]nonnegative
• A147716 → basis A013610
  1 · 15, 3 · 225, 90, 9 · 3375, 2025, 405, 27 … Σ 1, 18, 324, 5832, 104976, 1889568, …
  (−∞, 0]nonnegativerational roots
• A038325: Triangle read by rows whose (i,j)-th entry is binomial(i,j)*11^(i-j)*11^j.
  1 · 11, 11 · 121, 242, 121 · 1331, 3993, 3993, 1331 … Σ 1, 22, 484, 10648, 234256, 5153632, …
  (−∞, 0)nonnegativerational roots
• A154602: Exponential Riordan array [exp(sinh(x)*exp(x)), sinh(x)*exp(x)].
  1 · 1, 1 · 3, 4, 1 · 11, 19, 9, 1 … Σ 1, 2, 8, 40, 240, 1664, 12992, 112256, …
  (−∞, −1]nonnegative