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A223256 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. 2
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 (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 A001008, corresponding to the fact that the matrix J(n) above has trace equal to the n-th harmonic number.

See A223257 for denominators.

LINKS

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

Wikipedia, Jacobi coordinates

EXAMPLE

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,

...

CROSSREFS

Sequence in context: A257894 A103997 A256895 * A013561 A176468 A176421

Adjacent sequences:  A223253 A223254 A223255 * A223257 A223258 A223259

KEYWORD

easy,frac,nonn,tabl

AUTHOR

Alberto Tacchella, Mar 18 2013

STATUS

approved

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Last modified September 21 23:55 EDT 2019. Contains 327286 sequences. (Running on oeis4.)