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A223257 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. 2
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

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.

See A223256 for numerators.

LINKS

Table of n, a(n) for n=0..54.

Wikipedia, Jacobi coordinates

EXAMPLE

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,

...

CROSSREFS

Sequence in context: A075798 A155864 A145903 * A173881 A329228 A172373

Adjacent sequences:  A223254 A223255 A223256 * A223258 A223259 A223260

KEYWORD

easy,frac,nonn,tabl

AUTHOR

Alberto Tacchella, Mar 18 2013

STATUS

approved

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Last modified December 4 15:14 EST 2021. Contains 349526 sequences. (Running on oeis4.)