A350149 -id:A350149 - cp's OEIS frontend

1, 1, 0, 2, 2, 1, 6, 12, 12, 8, 24, 72, 108, 108, 81, 120, 480, 960, 1280, 1280, 1024, 720, 3600, 9000, 15000, 18750, 18750, 15625, 5040, 30240, 90720, 181440, 272160, 326592, 326592, 279936, 40320, 282240, 987840, 2304960, 4033680, 5647152, 6588344, 6588344, 5764801

Offset: 0

Robert B Fowler, Dec 23 2021

Rows n >= 2 are coefficients in a double summation power series for the integral of x^(1/x), and the integral of its inverse function y^(y^(y^(y^(...)))). See A350358.

			Triangle T(n,k) begins:
  -----------------------------------------------------------------
   n\k     0      1      2       3       4       5       6       7
  -----------------------------------------------------------------
   0  |    1,
   1  |    1,     0,
   2  |    2,     2,     1,
   3  |    6,    12,    12,      8,
   4  |   24,    72,   108,    108,     81,
   5  |  120,   480,   960,   1280,   1280,   1024,
   6  |  720,  3600,  9000,  15000,  18750,  18750,  15625,
   7  | 5040, 30240, 90720, 181440, 272160, 326592, 326592, 279936.
  ...

Cf. A000142 (first column), A062119 (second column), A065440 (main diagonal), A055897 (subdiagonal), A217701 (row sums).
Cf. A350269, A350358.
Cf. A061711, A350149.

T := (n, k) -> (n!/k!)*(n - 1)^k:
seq(seq(T(n, k), k = 0..n), n = 0..8); # Peter Luschny, Dec 24 2021

T[1, 0] := 1; T[n_, k_] := n!*(n - 1)^k/k!; Table[T[n, k], {n, 0, 8}, {k, 0, n}] // Flatten (* Amiram Eldar, Dec 24 2021 *)

T(n, k) = binomial(n, k)*A350269(n, k). - Peter Luschny, Dec 25 2021

T(n+1, k) = A061711(n) * (n+1) / A350149(n, k). - Robert B Fowler, Jan 11 2022

cp's OEIS Frontend

A350297 Triangle read by rows: T(n,k) = n!*(n-1)^k/k!.

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