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

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.

Links

Table of n, a(n) for n=0..44.

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).

Cf. A350269, A350358.

Cf. A061711, A350149.

Sequence in context: A362708 A138678 A335997 * A181731 A278792 A343807

Adjacent sequences: A350294 A350295 A350296 * A350298 A350299 A350300

Keyword

easy,nonn,tabl

Author

Robert B Fowler, Dec 23 2021

Status

approved