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Triangle n!/(n-k), 1 <= k < n, read by rows.
3

%I #23 Sep 10 2023 01:52:45

%S 2,3,6,8,12,24,30,40,60,120,144,180,240,360,720,840,1008,1260,1680,

%T 2520,5040,5760,6720,8064,10080,13440,20160,40320,45360,51840,60480,

%U 72576,90720,120960,181440,362880,403200,453600,518400,604800,725760,907200,1209600,1814400,3628800

%N Triangle n!/(n-k), 1 <= k < n, read by rows.

%C Together with 1, numbers n such that n divides k! if and only if k! >= n. - _Charles R Greathouse IV_, Aug 16 2016

%H Andrew Howroyd, <a href="/A058298/b058298.txt">Table of n, a(n) for n = 2..1276</a>

%H Florian Unger and Jonathan Krebs, <a href="https://arxiv.org/abs/2309.02938">MCMC Sampling of Directed Flag Complexes with Fixed Undirected Graphs</a>, arXiv:2309.02938 [math.ST], 2023.

%e Triangle begins:

%e 2;

%e 3, 6;

%e 8, 12, 24;

%e 30, 40, 60, 120;

%e 144, 180, 240, 360, 720;

%e 840, 1008, 1260, 1680, 2520, 5040;

%e 5760, 6720, 8064, 10080, 13440, 20160, 40320;

%e 45360, 51840, 60480, 72576, 90720, 120960, 181440, 362880;

%e ...

%t Flatten[Table[n!/(n-k),{n,2,10},{k,n-1}]] (* _Harvey P. Dale_, Jul 23 2014 *)

%o (PARI) T(n,k)={if(k<n, n!/(n-k), 0)} \\ _Andrew Howroyd_, Aug 08 2020

%Y Columns k=1..5 are A001048(n-1), A052747, A052759, A052778, A052794.

%Y Row sums are A052881.

%Y Cf. A077012.

%K easy,tabl,nonn

%O 2,1

%A _Leroy Quet_, Dec 07 2000