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A350297
Triangle read by rows: T(n,k) = n!*(n-1)^k/k!.
2
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
0,4
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
T(n+1, k) = A061711(n) * (n+1) / A350149(n, k). - Robert B Fowler, Jan 11 2022
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
Cf. A000142 (first column), A062119 (second column), A065440 (main diagonal), A055897 (subdiagonal), A217701 (row sums).
Sequence in context: A362708 A138678 A335997 * A181731 A278792 A343807
KEYWORD
easy,nonn,tabl
AUTHOR
Robert B Fowler, Dec 23 2021
STATUS
approved