A077012 - OEIS

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

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OFFSET

1,3

COMMENTS

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

LINKS

Table of n, a(n) for n=1..45.

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

EXAMPLE

Triangle begins:

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;

...

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 *)

CROSSREFS

Row sums give A000254.

Cf. A058298, A078921, A137853, A196533.

Sequence in context: A121457 A093784 A035560 * A078921 A011961 A182713

Adjacent sequences: A077009 A077010 A077011 * A077013 A077014 A077015

KEYWORD

nonn,tabl

AUTHOR

Amarnath Murthy, Oct 26 2002

EXTENSIONS

More terms from Sascha Kurz, Jan 26 2003

STATUS

approved