OFFSET
0,3
FORMULA
Conjectures: (Start)
T(n, 0) = A000045(n+1) for n >= 0.
T(n, 1) = 0 for n >= 0.
Sum_{j=0..2*(floor(k/2)+1)} A084610(floor(k/2)+1, j)*T(n+j, k) = 0 for n >= b(k), k >= 0 where b(k) is some nonnegative integer sequence (with a single exception at k = 1).
G.f. for k-th column is Q_k(x)/(1-x-x^2)^(floor(k/2)+1) for k >= 0 where Q_k(x) is some family of polynomials (with a single exception at k = 1). (End)
EXAMPLE
Irregular table begins:
1;
1;
2;
3, 0, -1;
5, 0, -2, -1;
8, 0, -5, -2, 0, 0, 0, 1;
13, 0, -10, -5, 1, 0, 0, 2, 0, 1;
21, 0, -20, -10, 3, 2, 0, 5, 0, 2, 0, 0, 0, 0, 0, -1;
34, 0, -38, -20, 9, 6, 1, 10, 0, 3, 0, 0, 0, 0, 0, -2, 0, 0, -1;
PROG
(PARI)
f(n) = if(n%2, (n-1)/2, n)
rows_upto(n) = my(v1); v1 = vector(n+1, i, 1); for(i=2, n, for(j=i+1, n+1, v1[j] = v1[i] + (-1)^(j-i+1)*z^f(j-i)*v1[j])); v1 = vector(n+1, i, Vecrev(v1[i]))
CROSSREFS
KEYWORD
sign,tabf
AUTHOR
Mikhail Kurkov, Sep 29 2024
STATUS
approved