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

2, 3, 6, 8, 12, 24, 30, 40, 60, 120, 144, 180, 240, 360, 720, 840, 1008, 1260, 1680, 2520, 5040, 5760, 6720, 8064, 10080, 13440, 20160, 40320, 45360, 51840, 60480, 72576, 90720, 120960, 181440, 362880, 403200, 453600, 518400, 604800, 725760, 907200, 1209600, 1814400, 3628800

Offset: 2

Author

Leroy Quet, Dec 07 2000

Keywords

• easy
• tabl
• nonn

Comments

Together with 1, numbers n such that n divides k! if and only if k! >= n. - Charles R Greathouse IV, Aug 16 2016

Examples

			Triangle begins:
      2;
      3,     6;
      8,    12,    24;
     30,    40,    60,   120;
    144,   180,   240,   360,   720;
    840,  1008,  1260,  1680,  2520,   5040;
   5760,  6720,  8064, 10080, 13440,  20160,  40320;
  45360, 51840, 60480, 72576, 90720, 120960, 181440, 362880;
  ...
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 2..1276
• Florian Unger and Jonathan Krebs, MCMC Sampling of Directed Flag Complexes with Fixed Undirected Graphs, arXiv:2309.02938 [math.ST], 2023.

Crossrefs

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

Row sums are A052881.

Cf. A019739. A077012.

Programs

Mathematica

Flatten[Table[n!/(n-k),{n,2,10},{k,n-1}]] (* Harvey P. Dale, Jul 23 2014 *)

PARI

T(n,k)={if(kAndrew Howroyd, Aug 08 2020

Formula

Sum_{n>=2} Sum_{k=1..n-1} 1/T(n, k) = e/2 (A019739). - Amiram Eldar, Jun 29 2025