A375761 Infinite triangle T(n, k), n > 0, k = 1..n, read and filled in the greedy way by rows with distinct positive integers such that for any n > 1, k = 2..n, T(n, k) = T(n-1, k-1) * T(n, k-1).

2, 3, 6, 4, 12, 72, 5, 20, 240, 17280, 7, 35, 700, 168000, 2903040000, 8, 56, 1960, 1372000, 230496000000, 669139107840000000000, 10, 80, 4480, 8780800, 12047257600000, 2776844687769600000000000, 1858095376984393503473664000000000000000000000

Offset: 1

Author

Rémy Sigrist, Aug 27 2024

Keywords

• nonn
• tabl

Comments

This sequence is a variant of A035312, based on products instead of sums.

The value 1 cannot appear (as it would imply a duplicate term).

We can always start a new row with a prime number that does not divide prior terms, so the sequence is well defined.

Will every integer > 1 appear in the sequence?

Examples

			Triangle T(n, k) begins:
               2
           3      6
         4   12      72
       5  20    240      17280
     7  35  700    168000    2903040000
    8 56 1960 1372000 230496000000 669139107840000000000
		

Links

• Rémy Sigrist, PARI program

Crossrefs

Cf. A035312, A064319, A066117, A375846 (right border), A375857 (left border).

Programs

PARI

\\ See Links section.