OFFSET
0,7
COMMENTS
Row n has length 1 + binomial(n,2) and sum A000110(n) (a Bell number).
LINKS
Alois P. Heinz, Rows n = 0..50, flattened
A. M. Baxter, Algorithms for Permutation Statistics, Ph. D. Dissertation, Rutgers University, May 2011.
Andrew Baxter, Additional terms, formatted as a table.
Andrew M. Baxter and Lara K. Pudwell, Enumeration schemes for dashed patterns, arXiv preprint arXiv:1108.2642, 2011
EXAMPLE
Triangle begins:
1
1
1 1
1 1 2 1
1 1 2 4 3 3 1
1 1 2 4 7 8 9 9 6 4 1
...
MAPLE
b:= proc(u, o) option remember; expand(`if`(u+o=0, 1,
add(b(u-j, o+j-1)*x^(o+j-1), j=1..u)+
add(`if`(u=0, b(u+j-1, o-j)*x^(o-j), 0), j=1..o)))
end:
T:= n-> (p-> seq(coeff(p, x, i), i=0..degree(p)))(b(0, n)):
seq(T(n), n=0..10); # Alois P. Heinz, Nov 14 2015
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
N. J. A. Sloane, Apr 13 2011
EXTENSIONS
More terms from Andrew Baxter, May 17 2011.
STATUS
approved