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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

Table of n, a(n) for n=0..53.

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.)