A114423 Multifactorial array read by ascending antidiagonals.

1, 1, 1, 2, 1, 1, 6, 2, 1, 1, 24, 3, 2, 1, 1, 120, 8, 3, 2, 1, 1, 720, 15, 4, 3, 2, 1, 1, 5040, 48, 10, 4, 3, 2, 1, 1, 40320, 105, 18, 5, 4, 3, 2, 1, 1, 362880, 384, 28, 12, 5, 4, 3, 2, 1, 1, 3628800, 945, 80, 21, 6, 5, 4, 3, 2, 1, 1, 39916800, 3840, 162, 32, 14, 6, 5, 4, 3, 2, 1, 1

Offset: 0

Author

Jonathan Vos Post, Feb 12 2006

Keywords

• nonn
• easy
• tabl

Comments

The columns are n!, n!!, n!!!, ... n!k for n >= 0, k >= 1.

Examples

			Table M begins:
  n / M(n,k)
  0 |   1   1   1   1   1
  1 |   1   1   1   1   1
  2 |   2   2   2   2   2
  3 |   6   3   3   3   3
  4 |  24   8   4   4   4
  5 | 120  15  10   5   5
  6 | 720  48  18  12   6
		

Links

• Eric Weisstein's World of Mathematics, Multifactorial.

Crossrefs

Cf. A000142 (n!), A006882 (n!!), A007661 (n!!!), A007662(n!4), A085157 (n!5), A085158 (n!6), A114799 (n!7), A114800 (n!8), A114806 (n!9), A288327 (n!10).

Cf. A129116 (transposed).

Programs

Mathematica

NFactorialM[n_, m_] := Block[{k = n, p = Max[1, n]},
     While[k > m, k -= m; p *= k]; p];
Table[NFactorialM[n - m + 1, m], {n, 1, 11}, {m, 1, n}] // Flatten (* Jean-François Alcover, Aug 01 2021, after Robert G. Wilson v in A007662 *)

Formula

M(n,k) = n!k.

M(n,k) = A129116(k,n). - Georg Fischer, Nov 02 2021

Extensions

Edited by Alois P. Heinz, Apr 24 2025