A114423 - OEIS

%I #22 Nov 02 2021 11:51:51

%S 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,

%T 40320,105,18,5,4,3,2,1,362880,384,28,12,5,4,3,2,1,3628800,945,80,21,

%U 6,5,4,3,2,1,39916800,3840,162,32,14,6,5,4,3,2,1

%N Multifactorial array read by ascending antidiagonals.

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

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Multifactorial.html">Multifactorial.</a>

%F M(n,k) = n!k.

%F M(n,k) = A129116(k,n). - _Georg Fischer_, Nov 02 2021

%e Table M begins:

%e n / M(n,k)

%e 1.|...1...1...1...1...1

%e 2.|...2...2...2...2...2

%e 3.|...6...3...3...3...3

%e 4.|..24...8...4...4...4

%e 5.|.120..15..10...5...5

%e 6.|.720..48..18..12...6

%t NFactorialM[n_, m_] := Block[{k = n, p = Max[1, n]},

%t      While[k > m, k -= m; p *= k]; p];

%t 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 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 Cf. A129116 (transposed).

%K easy,nonn,tabl

%O 1,2

%A _Jonathan Vos Post_, Feb 12 2006