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1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 4, 4, 2, 4, 4, 4, 1, 1, 3, 12, 12, 6, 6, 12, 12, 3, 1, 1, 1, 3, 12, 6, 6, 6, 12, 3, 1, 1, 1, 1, 1, 3, 6, 6, 6, 6, 3, 1, 1, 1, 1, 2, 2, 2, 3, 12, 12
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OFFSET
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0,12
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COMMENTS
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We assume that A085056(0)=1 since it would be the empty product.
These are the generalized binomial coefficients associated with the sequence A003557.
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LINKS
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FORMULA
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EXAMPLE
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The first five terms in A003557 are: 1, 1, 1, 2, 1 and so T(4,2) = 2*1*1*1/((1*1)*(1*1))=2 and T(5,4) = 1*2*1*1*1/((2*1*1*1)*(1))=1.
The triangle begins:
1,
1, 1,
1, 1, 1,
1, 1, 1, 1,
1, 2, 2, 2, 1,
1, 1, 2, 2, 1, 1,
1, 1, 1, 2, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1,
1, 4, 4, 4, 2, 4, 4, 4, 1,
1, 3, 12, 12, 6, 6, 12, 12, 3, 1.
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PROG
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(Sage)
q=100 #change q for more rows
P=[0]+[n/prod([x for x in prime_divisors(n)]) for n in [1..q]]
[[prod(P[1:n+1])/(prod(P[1:k+1])*prod(P[1:(n-k)+1])) for k in [0..n]] for n in [0..len(P)-1]] # generates the triangle up to q rows.
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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