cp's OEIS Frontend

A114423 Multifactorial array read by ascending antidiagonals.

%I A114423 #27 Apr 24 2025 08:45:08
%S A114423 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,
%T A114423 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,
%U A114423 1,3628800,945,80,21,6,5,4,3,2,1,1,39916800,3840,162,32,14,6,5,4,3,2,1,1
%N A114423 Multifactorial array read by ascending antidiagonals.
%C A114423 The columns are n!, n!!, n!!!, ... n!k for n >= 0, k >= 1.
%H A114423 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Multifactorial.html">Multifactorial.</a>
%F A114423 M(n,k) = n!k.
%F A114423 M(n,k) = A129116(k,n). - _Georg Fischer_, Nov 02 2021
%e A114423 Table M begins:
%e A114423   n / M(n,k)
%e A114423   0 |   1   1   1   1   1
%e A114423   1 |   1   1   1   1   1
%e A114423   2 |   2   2   2   2   2
%e A114423   3 |   6   3   3   3   3
%e A114423   4 |  24   8   4   4   4
%e A114423   5 | 120  15  10   5   5
%e A114423   6 | 720  48  18  12   6
%t A114423 NFactorialM[n_, m_] := Block[{k = n, p = Max[1, n]},
%t A114423      While[k > m, k -= m; p *= k]; p];
%t A114423 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 *)
%Y A114423 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).
%Y A114423 Cf. A129116 (transposed).
%K A114423 nonn,easy,tabl
%O A114423 0,4
%A A114423 _Jonathan Vos Post_, Feb 12 2006
%E A114423 Edited by _Alois P. Heinz_, Apr 24 2025