OFFSET
0,5
LINKS
Alois P. Heinz, Rows n = 0..60, flattened
EXAMPLE
T(4,1) = 7: 1234, 1324, 1423, 2314, 2413, 3412, 4321.
Triangle T(n,k) begins:
1;
0, 1;
0, 2;
0, 2, 4;
0, 7, 17;
0, 2, 118;
0, 82, 436, 202;
0, 2, 3294, 1744;
0, 1456, 18164, 20700;
0, 1515, 140659, 220706;
0, 50774, 1096994, 2317340, 163692;
0, 2, 10116767, 27136103, 2663928;
0, 3052874, 94670868, 328323746, 52954112;
...
MAPLE
b:= proc(u, o, t, s) option remember;
`if`(u+o=0, x^(nops(s union {t})-1),
add(b(u-j, o+j-1, 1, s union {t}), j=1..u)+
add(b(u+j-1, o-j, t+1, s), j=1..o))
end:
T:= n-> (p-> seq(coeff(p, x, i), i=0..degree(p)))(b(n, 0$2, {})):
seq(T(n), n=0..16);
MATHEMATICA
b[u_, o_, t_, s_] := b[u, o, t, s] = If[u + o == 0, x^(Length[s ~Union~ {t}] - 1), Sum[b[u - j, o + j - 1, 1, s ~Union~ {t}], {j, 1, u}] + Sum[b[u + j - 1, o - j, t + 1, s], {j, 1, o}]];
T[n_] := With[{p = b[n, 0, 0, {}]}, Table[Coefficient[p, x, i], {i, 0, Exponent[p, x]}]];
T /@ Range[0, 16] // Flatten (* Jean-François Alcover, Jan 27 2021, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Alois P. Heinz, Jul 25 2018
STATUS
approved