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 A129453 An analog of Pascal's triangle based on A092287. T(n,k) = A092287(n)/(A092287(n-k)*A092287(k)), 0 <= k <= n. 2
 1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 16, 24, 16, 1, 1, 5, 40, 40, 5, 1, 1, 864, 2160, 11520, 2160, 864, 1, 1, 7, 3024, 5040, 5040, 3024, 7, 1, 1, 2048, 7168, 2064384, 645120, 2064384, 7168, 2048, 1, 1, 729, 746496, 1741824, 94058496, 94058496, 1741824, 746496, 729 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS It appears that the T(n,k) are always integers. This would follow from the conjectured prime factorization given in A092287. Calculation suggests that the binomial coefficients C(n,k) divide T(n,k) and indeed that T(n,k)/C(n,k) are perfect squares. LINKS FORMULA T(n,k)=product_{i=1..n}product_{j=1..n} gcd(i,j)/(product_{i=1..n-k}product_{j=1..n-k} gcd(i,j)*product_{i=1..k}product_{j=1..k} gcd(i,j)) - empty products are to be taken equal to 1. EXAMPLE Triangle starts: 1 1 1 1 2 1 1 3 3 1 1 16 24 16 1 1 5 40 40 5 1 CROSSREFS Cf. A007318, A092287, A129454, A129455. Sequence in context: A129439 A176469 A141542 * A129455 A329322 A067924 Adjacent sequences:  A129450 A129451 A129452 * A129454 A129455 A129456 KEYWORD nonn,tabl AUTHOR Peter Bala, Apr 16 2007 STATUS approved

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Last modified June 15 15:16 EDT 2021. Contains 345049 sequences. (Running on oeis4.)