OFFSET
0,6
LINKS
Alois P. Heinz, Rows n = 0..80, flattened
Carlitz, L., Richard Scoville, and Theresa Vaughan, Enumeration of pairs of permutations and sequences, Bulletin of the American Mathematical Society 80.5 (1974): 881-884. [Annotated scanned copy]
L. Carlitz, N. J. A. Sloane, and C. L. Mallows, Correspondence, 1975
EXAMPLE
Triangle begins:
1;
1;
1, 1;
1, 8, 1;
1, 43, 43, 1;
1, 194, 826, 194, 1;
1, 803, 11284, 11284, 803, 1;
1, 3184, 127905, 392244, 127905, 3184, 1;
1, 12367, 1297629, 10258067, 10258067, 1297629, 12367, 1;
...
MAPLE
b:= proc(u, o, h) option remember; `if`(u+o=0, 1, expand(
add(add(b(u-j, o+j-1, h+i-1), i=1..u+o-h)*x, j=1..u)+
add(add(b(u+j-1, o-j, h-i), i=1..h), j=1..o)))
end:
T:= n-> (p-> seq(coeff(p, x, i), i=0..degree(p)))(b(0, n$2)):
seq(T(n), n=0..10); # Alois P. Heinz, Jul 02 2015
MATHEMATICA
b[u_, o_, h_] := b[u, o, h] = If[u+o == 0, 1, Expand[Sum[Sum[b[u-j, o+j-1, h+i-1], {i, 1, u+o-h}]*x, {j, 1, u}] + Sum[Sum[b[u+j-1, o-j, h-i], {i, 1, h}], {j, 1, o}]]]; T[n_] := Function[p, Table[Coefficient[p, x, i], {i, 0, Exponent[p, x]}]][b[0, n, n]]; Table[T[n], {n, 0, 10}] // Flatten (* Jean-François Alcover, Feb 12 2016, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
N. J. A. Sloane, Jun 30 2015, following a suggestion from L. Carlitz, Nov 30 1975.
EXTENSIONS
More terms from Alois P. Heinz, Jul 02 2015
STATUS
approved