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A223256
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Triangle read by rows: T(0,0)=1; for n>=1 T(n,k) is the numerator 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, 3, 1, 1, 11, 11, 1, 1, 25, 61, 25, 1, 1, 137, 379, 379, 137, 1, 1, 49, 667, 3023, 667, 49, 1, 1, 363, 529, 8731, 8731, 529, 363, 1, 1, 761, 46847, 62023, 270961, 62023, 46847, 761, 1, 1, 7129, 51011, 9161, 28525, 28525, 9161, 51011, 7129, 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 A001008, 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, 3, 1,
1, 11, 11, 1,
1, 25, 61, 25, 1,
1, 137, 379, 379, 137, 1,
1, 49, 667, 3023, 667, 49, 1,
1, 363, 529, 8731, 8731, 529, 363, 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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