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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).
3
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
1,1
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?
EXAMPLE
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
PROG
(PARI) \\ See Links section.
CROSSREFS
Cf. A035312, A064319, A066117, A375846 (right border), A375857 (left border).
Sequence in context: A119741 A268216 A346928 * A245712 A285331 A237125
KEYWORD
nonn,tabl
AUTHOR
Rémy Sigrist, Aug 27 2024
STATUS
approved