[seqfan] A092379 data discrepances

Jean-François Alcover jf.alcover at gmail.com
Wed Sep 12 10:08:07 CEST 2012


Dear SeqFans,

I have found discrepancies recomputing A092379 with this Mma program :

p[i_, j_] := Binomial[i+j-2, i-1];

cp[n_] := cp[n] = CharacteristicPolynomial[ Table[p[i, j], {i, 1, n}, {j,
1, n}], x];

c[k_, n_] := Coefficient[cp[n], x, k]//Abs;

q[n_?EvenQ, m_] := c[n/2 - m, n] + Sum[ c[n/2 - m - 2*r, n]*(m +
2*r)/(m+r)*Binomial[m+r, r], {r, 1, n/4 - m/2}];

q[n_?OddQ, m_] := Sum[(-1)^r* c[(n-1)/2 - m - 2*r, n] - c[(n-1)/2 - m - 2*r
- 1, n]*Binomial[m+r, r], {r, 0, (n-1)/4 - m/2}];

a[n_] := q[n, 7];

Table[a[n], {n, 14, 20}]

I hope someone could examine what I did and/or check
with a different language, to ensure correctness.
Thanks in advance
jfa



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