OFFSET
0,6
LINKS
Alois P. Heinz, Rows n = 0..140, flattened
EXAMPLE
T(6,1) = 8: partitions of 6 with largest multiplicity 1 are [3,2,1], [4,2], [5,1], [6], with 3+2+2+1 = 8 parts.
T(6,2) = 9: [2,2,1,1], [3,3], [4,1,1].
T(6,3) = 7: [2,2,2], [3,1,1,1].
T(6,4) = 5: [2,1,1,1,1].
T(6,5) = 0.
T(6,6) = 6: [1,1,1,1,1,1].
Triangle begins:
0;
0, 1;
0, 1, 2;
0, 3, 0, 3;
0, 3, 5, 0, 4;
0, 5, 6, 4, 0, 5;
0, 8, 9, 7, 5, 0, 6;
0, 10, 13, 13, 5, 6, 0, 7;
0, 13, 23, 14, 15, 6, 7, 0, 8;
...
MAPLE
b:= proc(n, i, k) option remember; `if`(n=0, [1, 0], `if`(i<1, [0, 0],
add((l->[l[1], l[2]+l[1]*j])(b(n-i*j, i-1, k)), j=0..min(n/i, k))))
end:
T:= (n, k)-> b(n, n, k)[2] -b(n, n, k-1)[2]:
seq(seq(T(n, k), k=0..n), n=0..12);
MATHEMATICA
b[n_, i_, k_] := b[n, i, k] = If[n == 0, {1, 0}, If[i < 1, {0, 0}, Sum[b[n-i*j, i-1, k] /. l_List :> {l[[1]], l[[2]] + l[[1]]*j}, {j, 0, Min[n/i, k]}]]]; T[_, 0] = 0; T[n_, k_] := b[n, n, k][[2]] - b[n, n, k-1][[2]]; Table[Table[T[n, k], {k, 0, n}], {n, 0, 12}] // Flatten (* Jean-François Alcover, Dec 27 2013, translated from Maple *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Alois P. Heinz, Feb 27 2013
STATUS
approved