OFFSET
0,14
LINKS
Alois P. Heinz, Rows n = 0..500, flattened
EXAMPLE
T(10,1) = 1: [10].
T(10,2) = 4: [5,5], [4,6], [3,7], [2,8].
T(10,3) = 3: [3,3,4], [2,4,4], [2,3,5].
Triangle T(n,k) begins:
1;
0;
0, 1;
0, 1;
0, 1;
0, 1, 1;
0, 1, 2;
0, 1, 2;
0, 1, 3;
0, 1, 3, 1;
0, 1, 4, 3;
0, 1, 4, 4;
0, 1, 5, 6;
0, 1, 5, 7;
0, 1, 6, 9, 1;
...
MAPLE
b:= proc(n, i) option remember; `if`(n=0, 1,
`if`(i<1, 0, b(n, i-1)+`if`(i>n, 0, (p-> expand(
x*(p-coeff(p, x, i-1)*x^(i-1))))(b(n-i, i)))))
end:
T:= n-> (p-> seq(coeff(p, x, i), i=0..max(0, degree(p))))(b(n$2)):
seq(T(n), n=0..30);
MATHEMATICA
b[n_, i_] := b[n, i] = If[n==0, 1, If[i<1, 0, b[n, i-1] + If[i>n, 0, Function[p, Expand[x*(p - Coefficient[p, x, i-1]*x^(i-1))]][b[n-i, i]]]] ]; T[n_] := Function[p, Table[Coefficient[p, x, i], {i, 0, Max[0, Exponent[p, x]]}]][b[n, n]]; Table[T[n], {n, 0, 30}] // Flatten (* Jean-François Alcover, Feb 08 2017, translated from Maple *)
CROSSREFS
KEYWORD
AUTHOR
Alois P. Heinz, Feb 26 2014
STATUS
approved