A077012 Triangle in which n-th row contains all possible products of n-1 of the first n natural numbers in ascending order.

1, 1, 2, 2, 3, 6, 6, 8, 12, 24, 24, 30, 40, 60, 120, 120, 144, 180, 240, 360, 720, 720, 840, 1008, 1260, 1680, 2520, 5040, 5040, 5760, 6720, 8064, 10080, 13440, 20160, 40320, 40320, 45360, 51840, 60480, 72576, 90720, 120960, 181440, 362880

Offset: 1

Author

Amarnath Murthy, Oct 26 2002

Keywords

• nonn
• tabl

Comments

Row products of A137853. - Mats Granvik, Jun 24 2009

Examples

			Triangle begins:
     1;
     1,    2;
     2,    3,    6;
     6,    8,   12,   24;
    24,   30,   40,   60,   120;
   120,  144,  180,  240,   360,   720;
   720,  840, 1008, 1260,  1680,  2520,  5040;
  5040, 5760, 6720, 8064, 10080, 13440, 20160, 40320;
  ...
		

Crossrefs

Row sums give A000254.

Cf. A058298, A078921, A137853, A196533.

Programs

Maple

A077012_row := proc(n) local k; seq(n!/(n-k),k=0..n-1) end:
seq(print(A077012_row(n)),n=1..9); # Peter Luschny, Mar 21 2011

Mathematica

Flatten[Table[n!/(n-k),{n,10},{k,0,n-1}]] (* Harvey P. Dale, Dec 25 2011 *)

Formula

E.g.f.: -log(1-x)/(1-y*x). - Vladeta Jovovic, Feb 07 2003

Sum_{n>=1} Sum_{k=0..n-1} 1/T(n, k) = 3*e/2 (= A196533 / 10). - Amiram Eldar, Jun 29 2025

Extensions

More terms from Sascha Kurz, Jan 26 2003