OFFSET
1,3
COMMENTS
LINKS
Alois P. Heinz, Rows n = 1..200, flattened
EXAMPLE
For the partition [3,2^2], there are 3 objects in the part of size 3 and 4 objects in the parts of size 2, so this partition is counted towards T(7,4).
Triangle T(n,k) begins:
1;
0, 2;
0, 1, 2;
0, 1, 1, 3;
0, 0, 3, 2, 2;
0, 0, 2, 4, 1, 4;
0, 0, 1, 6, 3, 3, 2;
0, 0, 1, 6, 4, 6, 1, 4;
0, 0, 0, 6, 7, 8, 3, 3, 3;
0, 0, 0, 5, 7, 14, 4, 6, 2, 4;
0, 0, 0, 5, 7, 18, 7, 9, 5, 3, 2;
0, 0, 0, 3, 10, 22, 9, 14, 6, 6, 1, 6;
...
MAPLE
b:= proc(n, i, m) option remember; `if`(n=0 or i=1, x^
max(m, n), add(b(n-i*j, i-1, max(m, i*j)), j=0..n/i))
end:
T:= n-> (p-> seq(coeff(p, x, i), i=1..n))(b(n$2, 0)):
seq(T(n), n=1..20); # Alois P. Heinz, Feb 07 2020
MATHEMATICA
b[n_, i_, m_] := b[n, i, m] = If[n == 0 || i == 1, x^Max[m, n], Sum[b[n - i j, i - 1, Max[m, i j]], {j, 0, n/i}]];
T[n_] := Table[Coefficient[b[n, n, 0], x, i], {i, 1, n}];
Array[T, 20] // Flatten (* Jean-François Alcover, Nov 10 2020, after Alois P. Heinz *)
CROSSREFS
AUTHOR
Franklin T. Adams-Watters, Feb 04 2008
STATUS
approved