OFFSET
0,7
LINKS
Alois P. Heinz, Rows n = 0..40, flattened
Brian Drake, Limits of areas under lattice paths, Discrete Math. 309 (2009), no. 12, 3936-3953. See Example 3.
EXAMPLE
Triangle begins
1
1 1
1 1 1 2 1
1 1 1 3 3 4 3 3 3 1
1 1 1 3 3 5 6 8 9 11 12 11 10 7 6 4 1
...
MAPLE
b:= proc(x, y) option remember; expand(`if`(y>x or y<0, 0,
`if`(x=0, 1, b(x-1, y)*z^(2*y)+b(x, y-1)+`if`(y>0, add(
b(x-(2*j-1), y-1)*z^((2*y-1)*(2*j-1)), j=1..1+(x-y)/2), 0))))
end:
T:= n-> (p-> seq(coeff(p, z, i), i=0..degree(p)))(b(n$2)):
seq(T(n), n=0..8); # Alois P. Heinz, Feb 02 2018
MATHEMATICA
b[x_, y_] := b[x, y] = Expand[If[y > x || y < 0, 0, If[x == 0, 1, b[x - 1, y]*z^(2*y) + b[x, y - 1] + If[y > 0, Sum[b[x - (2*j - 1), y - 1]*z^((2*y - 1)*(2*j - 1)), {j, 1, 1 + (x - y)/2}], 0]]]];
T[n_] := Function[p, Table[Coefficient[p, z, i], {i, 0, Exponent[p, z]}]][ b[n, n]];
Table[T[n], {n, 0, 8}] // Flatten (* Jean-François Alcover, Jun 11 2018, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
N. J. A. Sloane, Nov 26 2011
EXTENSIONS
More term from Alois P. Heinz, Feb 02 2018
STATUS
approved