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A129455 An analog of Pascal's triangle based on A129454. T(n,k)= A129454(n)/(A129454(n-k)*A129454(k)). 3
1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 256, 384, 256, 1, 1, 5, 640, 640, 5, 1, 1, 1146617856, 2866544640, 244611809280, 2866544640, 1146617856, 1, 1, 7, 4013162496, 6688604160, 6688604160, 4013162496, 7, 1, 1, 35184372088832, 123145302310912 (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 A129454. Calculation suggests that the binomial coefficients C(n,k) divide T(n,k) and that T(n,k)/C(n,k) are perfect sixth powers.

LINKS

Table of n, a(n) for n=0..38.

FORMULA

T(n,k) = product_{h=1..n}product_{i=1..n}product_{j=1..n} gcd(h,i,j)/(product_{h=1..n-k}product_{i=1..n-k}product_{j=1..n-k} gcd(h,i,j)*product_{h=1..k}product_{i=1..k}product_{j=1..k} gcd(h,i,j)).

EXAMPLE

Triangle starts:

1

1 1

1 2 1

1 3 3 1

1 256 384 256 1

CROSSREFS

Cf. A007318, A092287, A129453, A129454.

Sequence in context: A176469 A141542 A129453 * A329322 A067924 A344912

Adjacent sequences:  A129452 A129453 A129454 * A129456 A129457 A129458

KEYWORD

nonn,tabl

AUTHOR

Peter Bala, Apr 16 2007

STATUS

approved

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Last modified June 19 03:38 EDT 2021. Contains 345125 sequences. (Running on oeis4.)