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A058298 Triangle n!/(n-k), 1 <= k < n, read by rows.

%I A058298 #27 Jun 29 2025 02:23:45
%S A058298 2,3,6,8,12,24,30,40,60,120,144,180,240,360,720,840,1008,1260,1680,
%T A058298 2520,5040,5760,6720,8064,10080,13440,20160,40320,45360,51840,60480,
%U A058298 72576,90720,120960,181440,362880,403200,453600,518400,604800,725760,907200,1209600,1814400,3628800
%N A058298 Triangle n!/(n-k), 1 <= k < n, read by rows.
%C A058298 Together with 1, numbers n such that n divides k! if and only if k! >= n. - _Charles R Greathouse IV_, Aug 16 2016
%H A058298 Andrew Howroyd, <a href="/A058298/b058298.txt">Table of n, a(n) for n = 2..1276</a>
%H A058298 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.
%F A058298 Sum_{n>=2} Sum_{k=1..n-1} 1/T(n, k) = e/2 (A019739). - _Amiram Eldar_, Jun 29 2025
%e A058298 Triangle begins:
%e A058298       2;
%e A058298       3,     6;
%e A058298       8,    12,    24;
%e A058298      30,    40,    60,   120;
%e A058298     144,   180,   240,   360,   720;
%e A058298     840,  1008,  1260,  1680,  2520,   5040;
%e A058298    5760,  6720,  8064, 10080, 13440,  20160,  40320;
%e A058298   45360, 51840, 60480, 72576, 90720, 120960, 181440, 362880;
%e A058298   ...
%t A058298 Flatten[Table[n!/(n-k),{n,2,10},{k,n-1}]] (* _Harvey P. Dale_, Jul 23 2014 *)
%o A058298 (PARI) T(n,k)={if(k<n, n!/(n-k), 0)} \\ _Andrew Howroyd_, Aug 08 2020
%Y A058298 Columns k=1..5 are A001048(n-1), A052747, A052759, A052778, A052794.
%Y A058298 Row sums are A052881.
%Y A058298 Cf. A019739. A077012.
%K A058298 easy,tabl,nonn
%O A058298 2,1
%A A058298 _Leroy Quet_, Dec 07 2000