OFFSET
0,7
LINKS
Alois P. Heinz, Rows n = 0..24, flattened
FORMULA
EXAMPLE
T(4,0) = 5: 1234, 1432, 3214, 3412, 4231.
T(4,1) = 6: 2431, 3241, 3421, 4132, 4213, 4312.
T(4,2) = 10: 1243, 1324, 1342, 1423, 2134, 2314, 2413, 3124, 3142, 4321.
T(4,3) = 2: 2341, 4123.
T(4,4) = 1: 2143.
Triangle T(n,k) begins:
1;
1, 0;
1, 0, 1;
2, 0, 4, 0;
5, 6, 10, 2, 1;
21, 36, 42, 12, 9, 0;
117, 226, 219, 104, 47, 6, 1;
792, 1568, 1472, 800, 328, 64, 16, 0;
6205, 12360, 11596, 6652, 2658, 688, 148, 12, 1;
55005, 109760, 103600, 60840, 24770, 7120, 1560, 200, 25, 0;
...
MAPLE
b:= proc(s) option remember; expand((n-> `if`(n=0, 1, add(
`if`(abs(n-j)=1, x, 1)*b(s minus {j}), j=s)))(nops(s)))
end:
T:= n-> (p-> seq(coeff(p, x, i), i=0..n))(b({$1..n})):
seq(T(n), n=0..12);
MATHEMATICA
b[s_] := b[s] = Expand[With[{n = Length[s]}, If[n==0, 1, Sum[
If[Abs[n-j]==1, x, 1]*b[s~Complement~{j}], {j, s}]]]];
T[n_] := PadRight[CoefficientList[b[Range[n]], x], n+1];
T /@ Range[0, 12] // Flatten (* Jean-François Alcover, Feb 09 2021, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Alois P. Heinz, Jan 23 2019
STATUS
approved