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A223257
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Triangle read by rows: T(0,0)=1; for n>=1 T(n,k) is the denominator of the coefficient of x^k in the characteristic polynomial of the matrix realizing the transformation to Jacobi coordinates for a system of n particles on a line.
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2
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1, 1, 1, 1, 2, 1, 1, 6, 6, 1, 1, 12, 24, 12, 1, 1, 60, 120, 120, 60, 1, 1, 20, 180, 720, 180, 20, 1, 1, 140, 126, 1680, 1680, 126, 140, 1, 1, 280, 10080, 10080, 40320, 10080, 10080, 280, 1, 1, 2520, 10080, 1296, 3456, 3456, 1296, 10080, 2520, 1
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OFFSET
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0,5
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COMMENTS
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The matrix J(n) realizing the change of coordinates for n particles is
[1, -1, 0, 0, 0, ... 0],
[1/2, 1/2, -1, 0, ... 0],
[1/3, 1/3, 1/3, -1, 0 ... 0],
...
[1/n, 1/n, 1/n, 1/n, ... 1/n]
Diagonals T(n,1)=T(n,n-1) are A002805, corresponding to the fact that the matrix J(n) above has trace equal to the n-th harmonic number.
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LINKS
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EXAMPLE
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Triangle begins:
1,
1, 1,
1, 2, 1,
1, 6, 6, 1,
1, 12, 24, 12, 1,
1, 60, 120, 120, 60, 1,
1, 20, 180, 720, 180, 20, 1,
1, 140, 126, 1680, 1680, 126, 140, 1,
...
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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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