A001147

View A001147 at the OEIS

identification: the entry's rule defines the sequence for every index; tail: the sequence is the entry's tail after some prefix rows; match_*: finite agreement only.

• 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. (match row sums)
  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
• A288874: Row reversed version of triangle A201637 (second-order Eulerian triangle). (match row sums)
  A201637 → reverse (shift +1)
  1 · 0, 1 · 0, 2, 1 · 0, 6, 8, 1 … row sums 1, 1, 3, 15, 105, 945, 10395, 135135, …
  A288874 (−∞, 0] nonnegative
• A085881 → γ (match row sums)
  1 · 1 · 3 · 15 … row sums 1, 1, 3, 15, 105, 945, 10395, 135135, …
  (−∞, 0] nonnegative rational roots
• A130534 → x ↦ x/(x+1) (match row sums)
  1 · 1, 2 · 2, 7, 6 · 6, 29, 46, 24 … row sums 1, 3, 15, 105, 945, 10395, 135135, …
  [−1, 0] nonnegative rational roots
• A185410: A decomposition of the double factorials A001147. (match row sums)
  1 · 1 · 1, 2 · 1, 10, 4 … row sums 1, 1, 3, 15, 105, 945, 10395, 135135, …
  A185410 (−∞, 0) nonnegative
• A161198: Triangle of polynomial coefficients related to the series expansions of (1-x)^((-1-2*n)/2). (match row sums)
  1 · 1, 2 · 3, 8, 4 · 15, 46, 36, 8 … row sums 1, 3, 15, 105, 945, 10395, 135135, …
  A161198 (−∞, 0) nonnegative rational roots
• A059364: Triangle T(n,k)=Sum_{i=0..n} |stirling1(n,n-i)|*binomial(i,k), k=0..n-1. (match row sums)
  1 · 2, 1 · 6, 7, 2 · 24, 46, 29, 6 … row sums 1, 3, 15, 105, 945, 10395, 135135, …
  A059364 (−∞, −1] nonnegative rational roots
• A088996: Triangle T(n, k) read by rows: T(n, k) = Sum_{j=0..n} binomial(j, n-k) * |Stirling1(n, n-j)|. (match row sums)
  1 · 0, 1 · 0, 1, 2 · 0, 2, 7, 6 … row sums 1, 1, 3, 15, 105, 945, 10395, 135135, …
  A088996 [−1, 0] nonnegative rational roots
• A185411: A triangular decomposition of the double factorial numbers A001147. (match row sums)
  A185410 → reverse
  1 · 0, 1 · 0, 2, 1 · 0, 4, 10, 1 … row sums 1, 1, 3, 15, 105, 945, 10395, 135135, …
  A185411 (−∞, 0] nonnegative
• A102365 → x ↦ x+1 (match row sums)
  1 · 1 · 2, 1 · 7, 7, 1 … row sums 1, 1, 3, 15, 105, 945, 10395, 135135, …
  (−∞, −1] nonnegative
• A112007: Coefficient triangle for polynomials used for o.g.f.s for unsigned Stirling1 diagonals. (match row sums)
  1 · 2, 1 · 6, 8, 1 · 24, 58, 22, 1 … row sums 1, 3, 15, 105, 945, 10395, 135135, …
  A112007 (−∞, 0) nonnegative
• A008517: Second-order Eulerian triangle T(n,k), 1 <= k <= n. (match row sums)
  1 · 1, 2 · 1, 8, 6 · 1, 22, 58, 24 … row sums 1, 3, 15, 105, 945, 10395, 135135, …
  A008517 (−∞, 0) nonnegative
• A163936: Triangle related to the o.g.f.s. of the right-hand columns of A130534 (E(x,m=1,n)). (match row sums)
  1 · 1 · 2, 1 · 6, 8, 1 … row sums 1, 1, 3, 15, 105, 945, 10395, 135135, …
  A163936 (−∞, 0) nonnegative
• A201637: Triangle of second-order Eulerian numbers T(n,k) (n>=0, 0 <= k <= n) read by rows. (match row sums)
  1 · 1 · 1, 2 · 1, 8, 6 … row sums 1, 1, 3, 15, 105, 945, 10395, 135135, …
  A201637 (−∞, 0) nonnegative
• A028338 → basis A007318 (match row sums)
  1 · 2, 1 · 8, 6, 1 · 48, 44, 12, 1 … row sums 1, 3, 15, 105, 945, 10395, 135135, …
  (−∞, 0] nonnegative rational roots