A114423 Multifactorial array read by ascending antidiagonals.

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

Offset

1,2

Comments

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

Links

Table of n, a(n) for n=1..66.

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)
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: A114283 A106187 A110135 * A335109 A179863 A069123

Adjacent sequences: A114420 A114421 A114422 * A114424 A114425 A114426

Keyword

easy,nonn,tabl

Author

Jonathan Vos Post, Feb 12 2006

Status

approved