A340810 Triangle T(n,k), n>=2, 2 <= k <= A214046(n), read by rows, where T(n,k) = n! mod k^n.

2, 6, 8, 24, 24, 120, 16, 720, 48, 666, 5040, 128, 954, 40320, 384, 8586, 100736, 362880, 768, 26811, 483072, 3628800, 1280, 58725, 2168064, 39916800, 3072, 173259, 9239552, 234860975, 479001600

Offset: 2

Author

Seiichi Manyama, Jan 22 2021

Keywords

• nonn
• tabf

Examples

			n\k  |    2       3        4          5          6
-----+---------------------------------------------
   2 |    2;
   3 |    6;
   4 |    8,     24;
   5 |   24,    120;
   6 |   16,    720;
   7 |   48,    666,    5040;
   8 |  128,    954,   40320;
   9 |  384,   8586,  100736,    362880;
  10 |  768,  26811,  483072,   3628800;
  11 | 1280,  58725, 2168064,  39916800;
  12 | 3072, 173259, 9239552, 234860975, 479001600;
		

Links

• Seiichi Manyama, Rows n = 2..200, flattened

Crossrefs

Column k=2..4 give A068496, A212309, A212310.

Cf. A000142, A074184, A214046.

Programs

Mathematica

row[n_] := Module[{k = 1, s = {}}, While[k^n <= n!, k++; AppendTo[s, Mod[n!, k^n]]]; s]; Table[row[n], {n, 2, 12}] // Flatten (* Amiram Eldar, Apr 28 2021 *)

Ruby

def f(n)
  return 1 if n < 2
  (1..n).inject(:*)
end
def A(n)
  m = f(n)
  ary = []
  (2..n).each{|i|
    j = i ** n
    ary << m % j
    break if m <= j
  }
  ary
end
def A340810(n)
  (2..n).map{|i| A(i)}.flatten
end
p A340810(12)