A203989 - OEIS

A203989

Array: row n shows the coefficients of the characteristic polynomial of the n-th principal submatrix of {max(i,j)} (A051125).

1, -1, -2, -3, 1, 3, 11, 6, -1, -4, -23, -35, -10, 1, 5, 39, 98, 85, 15, -1, -6, -59, -207, -308, -175, -21, 1, 7, 83, 374, 795, 798, 322, 28, -1, -8, -111, -611, -1694, -2475, -1806, -546, -36, 1, 9, 143, 930, 3185, 6149, 6633, 3696, 870, 45

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OFFSET

1,3

COMMENTS

Let p(n)=p(n,x) be the characteristic polynomial of the n-th principal submatrix. The zeros of p(n) are real, and they interlace the zeros of p(n+1). See A202605 for a guide to related sequences.

The characteristic polynomial seems be the recurrence relation given by p(n,x) = -x * p(n-1,x) + n * (-1)^(n-1) * sum_{i=0..n-1} x^i * binomial(2n-i-2,i). - Enrique Pérez Herrero, Jan 29 2013

REFERENCES

(For references regarding interlacing roots, see A202605.)

LINKS

Table of n, a(n) for n=1..53.

EXAMPLE

Top of the array:

1... -1

-2... -3.... 1

3.... 11... 6... -1

-4... -23.. -35.. -10...1

5.... 39... 98... 85...15.. -1

MATHEMATICA