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

0,4

Comments

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

Links

Table of n, a(n) for n=0..77.

Eric Weisstein's World of Mathematics, Multifactorial.

Formula

M(n,k) = n!k.

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

Example

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

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 *)

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).

Sequence in context: A179380 A107106 A178249 * A119502 A142156 A136707

Adjacent sequences: A114420 A114421 A114422 * A114424 A114425 A114426

Keyword

nonn,easy,tabl

Author

Jonathan Vos Post, Feb 12 2006

Extensions

Edited by Alois P. Heinz, Apr 24 2025

Status

approved