OFFSET
0,4
COMMENTS
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.
FORMULA
T(n, k) = binomial(n, k)*A350269(n, k). - Peter Luschny, Dec 25 2021
EXAMPLE
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.
...
MAPLE
T := (n, k) -> (n!/k!)*(n - 1)^k:
seq(seq(T(n, k), k = 0..n), n = 0..8); # Peter Luschny, Dec 24 2021
MATHEMATICA
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 *)
CROSSREFS
KEYWORD
AUTHOR
Robert B Fowler, Dec 23 2021
STATUS
approved