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1381 sequences

• A227450 → θ+1
  2 · 2, 8 · 2, 24, 24 · 2, 56, 144, 64 … row sums 2, 10, 50, 266, 1522, 9354, 61490, …
  (−∞, 0] nonnegative
• A007318 → (1/2+(1/2)n)θ+1+n → reverse
  1 · 3, 2 · 6, 9, 3 · 10, 24, 18, 4 … row sums 1, 5, 18, 56, 160, 432, 1120, 2816, …
  (−∞, 0] nonnegative rational roots
• A143495 → (θ+1)²
  1 · 3, 4 · 9, 28, 9 · 27, 148, 108, 16 … row sums 1, 7, 46, 299, 1967, 13248, 91903, …
  (−∞, 0] nonnegative
• A103633 → (θ+1)²
  1 · 0, 4 · 0, 4, 9 · 0, 0, 9, 16 … row sums 1, 4, 13, 25, 66, 102, 248, 344, …
  (−∞, 0] nonnegative
• A039755 → (θ+1)²
  1 · 1, 4 · 1, 16, 9 · 1, 52, 81, 16 … row sums 1, 5, 26, 150, 964, 6836, 52936, …
  (−∞, 0] nonnegative
• A163932: Triangle related to the asymptotic expansion of E(x,m=3,n).
  A130534 → D²∘x (shift +1)
  1 · 3, 3 · 11, 18, 6 · 50, 105, 60, 10 … row sums 1, 6, 35, 225, 1624, 13132, 118124, …
  A163932 (−∞, 0] nonnegative
• A039755 → x ↦ x+1
  1 · 2, 1 · 6, 6, 1 · 24, 34, 12, 1 … row sums 1, 3, 13, 71, 457, 3355, 27509, 248127, …
  (−∞, −1] nonnegative
• A116412 → D
  1 · 6, 2 · 21, 18, 3 · 60, 90, 36, 4 … row sums 0, 1, 8, 42, 190, 797, 3192, 12391, …
  (−∞, 0] nonnegative
• A135838 → (θ+1)²
  1 · 2, 8 · 2, 16, 18 · 4, 48, 108, 64 … row sums 1, 10, 36, 224, 640, 3456, 8960, 45056, …
  (−∞, 0] nonnegative
• A007318 → (1/3+(1/2)n+(1/6)n²)θ+1+(3/2)n+(1/2)n² → reverse
  1 · 4, 3 · 10, 16, 6 · 20, 50, 40, 10 … row sums 1, 7, 32, 120, 400, 1232, 3584, 9984, …
  (−∞, 0] nonnegative rational roots
• A272866 → basis A007318
  1 · 5, 5, 1 · 25, 50, 35, 10, 1 … row sums 1, 11, 121, 1331, 14641, 161051, …
  (−∞, −1] nonnegative
• basis-map coefficients of A021012 → (θ+1)²
  1 · 0, -4 · 0, 0, 18 · 0, 0, 0, -96 … row sums 1, -4, 18, -96, 600, -4320, 35280, …
  (−∞, 0] rational roots
• basis-map coefficients of A026729 → basis A056242 → θ+1
  1 · 1, 4 · 1, 10, 12 · 1, 18, 48, 32 … row sums 1, 5, 23, 99, 408, 1632, 6388, 24596, …
  (−∞, 0] nonnegative
• A023531 → (θ+1)² → (θ+1)²
  1 · 0, 16 · 0, 0, 81 · 0, 0, 0, 256 … row sums 1, 16, 81, 256, 625, 1296, 2401, 4096, …
  (−∞, 0] nonnegative rational roots
• A008288 → θ+1
  1 · 1, 2 · 1, 6, 3 · 1, 10, 15, 4 … row sums 1, 3, 10, 30, 87, 245, 676, 1836, …
  (−∞, 0] nonnegative
• A207607 → D
  2 · 5, 4 · 9, 18, 6 · 14, 50, 39, 8 … row sums 0, 2, 9, 33, 111, 355, 1098, 3316, …
  (−∞, 0] nonnegative
• A053122 → x ↦ x+1
  1 · -1, 1 · 0, -2, 1 · 1, 1, -3, 1 … row sums 1, 0, -1, 0, 1, 0, -1, 0, …
  (−1, 3)
• basis-map coefficients of A371080, shifted → x ↦ x−1
  1 · -1, 1 · -2, 1, 1 · -10, 3, 6, 1 … row sums 1, 0, 0, 0, 0, 0, 0, 0, …
  (−∞, 1] rational roots
• A013611: Triangle of coefficients in expansion of (1+4x)^n.
  1 · 1, 4 · 1, 8, 16 · 1, 12, 48, 64 … row sums 1, 5, 25, 125, 625, 3125, 15625, 78125, …
  A013611 (−∞, 0) [−1, 0] nonnegative rational roots
• A062196 → (θ+1)²
  1 · 1, 12 · 1, 32, 54 · 1, 60, 270, 160 … row sums 1, 13, 87, 491, 2562, 12762, 61611, …
  (−∞, 0] nonnegative
• A007318 → basis A049020 → reverse
  1 · 1, 2 · 1, 5, 5 · 1, 9, 22, 15 … row sums 1, 3, 11, 47, 227, 1215, 7107, 44959, …
  (−∞, 0] nonnegative
• A131689 → D+1
  1 · 1, 1 · 1, 5, 2 · 1, 13, 24, 6 … row sums 1, 2, 8, 44, 308, 2612, 25988, 296564, …
  (−∞, 0] nonnegative
• A013620 → D+1
  1 · 5, 3 · 16, 30, 9 · 44, 144, 135, 27 … row sums 1, 8, 55, 350, 2125, 12500, 71875, …
  (−∞, 0] nonnegative rational roots
• A010054 → reverse → D+1
  1 · 3, 3 · 0, 12, 6 · 0, 0, 30, 10 … row sums 1, 6, 18, 40, 75, 126, 196, 288, …
  (−∞, 0] nonnegative rational roots
• A099093 → x ↦ x−12
  1 · -36, 3 · 1260, -213, 9 · -44064, 11232, -954, 27 … row sums 1, -33, 1056, -33759, 1079199, …
  (32/3, 12]
• A340556: E2(n, k), the second-order Eulerian numbers with E2(0, k) = δ_{0, k}. Triangle read by rows, E2(n, k) for 0 <= k <= n.
  A163936 → reverse
  1 · 0, 1 · 0, 1, 2 · 0, 1, 8, 6 … row sums 1, 1, 3, 15, 105, 945, 10395, 135135, …
  A340556 (−∞, 0] nonnegative
• A143685 → basis A007318
  1 · 2, 1 · 13, 13, 1 · 44, 66, 24, 1 … row sums 1, 3, 27, 135, 891, 5103, 31347, …
  (−∞, −1] nonnegative
• A053122 → D+1
  1 · -1, 1 · -1, -2, 1 · 6, -2, -3, 1 … row sums 1, 0, -2, 2, 1, -4, 3, 2, …
  (−∞, ∞)
• A081580 → D
  1 · 7, 2 · 13, 26, 3 · 19, 122, 57, 4 … row sums 0, 1, 9, 42, 202, 855, 3567, 14308, …
  (−∞, 0] nonnegative
• A143494 → (θ+1)²
  1 · 2, 4 · 4, 20, 9 · 8, 76, 81, 16 … row sums 1, 6, 33, 181, 1020, 5977, 36589, …
  (−∞, 0] nonnegative
• A063967 → x ↦ x−4
  1 · -3, 1 · 6, -5, 1 · -9, 15, -7, 1 … row sums 1, -2, 2, 0, -4, 8, -8, 0, …
  (−1, 3]
• A145324: Triangle read by rows: coefficients of 1; 1(X+2); 1(X+2)(X+3); 1(X+2)(X+3)(X+4); ....
  1 · 1, 2 · 1, 5, 6 · 1, 9, 26, 24 … row sums 1, 3, 12, 60, 360, 2520, 20160, 181440, …
  A145324 (−∞, 0) [−1, 0] nonnegative rational roots
• A064861 → D
  3, 4 · 5, 16, 12 · 6, 26, 36, 16 … row sums 7, 33, 84, 324, 756, 2700, 6048, 20736, …
  (−∞, 0] nonnegative rational roots
• A121574 → D+1
  1 · 3, 1 · 9, 7, 1 · 24, 32, 11, 1 … row sums 1, 4, 17, 68, 264, 1002, 3739, 13768, …
  (−∞, 0] nonnegative
• A062145 → θ+1
  1 · 1, 8 · 1, 20, 30 · 1, 36, 135, 80 … row sums 1, 9, 51, 252, 1170, 5247, 23023, …
  (−∞, 0] nonnegative
• A063967 → reverse
  1 · 1, 1 · 1, 3, 2 · 1, 5, 7, 3 … row sums 1, 2, 6, 16, 44, 120, 328, 896, …
  (−∞, 0] nonnegative
• A008292 → γ (scale 1/4) (shift +1) → x ↦ x+1
  1 · 2 · 6, 2 · 24, 16 … row sums 1, 2, 8, 40, 256, 1952, 17408, 177280, …
  (−∞, −1] nonnegative
• A039755 → D+1
  1 · 2, 1 · 5, 6, 1 · 14, 31, 12, 1 … row sums 1, 3, 12, 58, 324, 2044, 14320, 109960, …
  (−∞, 0] nonnegative
• A216973: Exponential Riordan array [x*exp(x),x].
  A007318 → D
  1 · 2, 2 · 3, 6, 3 · 4, 12, 12, 4 … row sums 0, 1, 4, 12, 32, 80, 192, 448, …
  A216973 (−∞, −1] nonnegative rational roots
• A207823: Triangle of coefficients of Chebyshev's S(n,x+4) polynomials (exponents of x in increasing order).
  1 · 4, 1 · 15, 8, 1 · 56, 46, 12, 1 … row sums 1, 5, 24, 115, 551, 2640, 12649, 60605, …
  A207823 (−6, −2) nonnegative
• A126351 → D
  2 · 5, 8 · 9, 38, 24 · 14, 110, 195, 64 … row sums 0, 2, 13, 71, 383, 2129, 12360, 75242, …
  (−∞, 0] nonnegative
• A007318 → ×(−(1/2)n+(1/2)n²) → D+1
  3, 4, 1 · 12, 27, 18, 3 · 30, 96, 108, 48, 6 … row sums 0, 0, 8, 60, 288, 1120, 3840, 12096, …
  (−∞, 0] nonnegative rational roots
• A102662 → D
  3 · 5, 6 · 7, 22, 9 · 9, 46, 51, 12 … row sums 0, 3, 11, 38, 118, 349, 997, 2780, …
  (−∞, 0] nonnegative
• A137338 → D+1
  1 · 0, 1 · -3, -1, 1 · 9, -6, -3, 1 … row sums 1, 1, -3, 1, 13, -61, 223, -867, …
  (−∞, ∞)
• A116414 → basis A007318
  1 · 5, 1 · 22, 10, 1 · 95, 69, 15, 1 … row sums 1, 6, 33, 180, 981, 5346, 29133, …
  (−9, −1) nonnegative
• A113214 → x ↦ x−2
  1 · 0, 1 · -2, -1, 1 · 4, -2, -2, 1 … row sums 1, 1, -2, 1, 1, -2, 1, 1, …
  (−2, 2]
• A249250 → D
  3 · 6, 6 · 9, 30, 9 · 12, 72, 72, 12 … row sums 0, 3, 12, 48, 168, 564, 1824, 5760, …
  (−∞, 0] nonnegative
• A008288 → D
  1 · 3, 2 · 5, 10, 3 · 7, 26, 21, 4 … row sums 0, 1, 5, 18, 58, 175, 507, 1428, …
  (−∞, 0] nonnegative
• A094816: Triangle read by rows: T(n,k) are the coefficients of Charlier polynomials: A046716 transposed, for 0 <= k <= n.
  1 · 1, 1 · 1, 3, 1 · 1, 8, 6, 1 … row sums 1, 2, 5, 16, 65, 326, 1957, 13700, …
  A094816 (−∞, 0) nonnegative
• A347056: Triangle read by rows: T(n,k) = (n+1)*(n+2)*(k+3)*binomial(n,k)/6, 0 <= k <= n.
  A007318 → (1/3+(1/2)n+(1/6)n²)θ+1+(3/2)n+(1/2)n²
  1 · 3, 4 · 6, 16, 10 · 10, 40, 50, 20 … row sums 1, 7, 32, 120, 400, 1232, 3584, 9984, …
  A347056 (−∞, 0] nonnegative rational roots