A373029 Triangle T(n,k), n >= 0, 0 <= k <= n, read by rows, where T(n,k) is the number of distinct partitions p of n such that max(p) is a multiple of k.
1, 0, 1, 0, 1, 1, 0, 2, 1, 1, 0, 2, 1, 1, 1, 0, 3, 1, 1, 1, 1, 0, 4, 2, 2, 1, 1, 1, 0, 5, 3, 1, 2, 1, 1, 1, 0, 6, 3, 1, 2, 2, 1, 1, 1, 0, 8, 4, 3, 2, 2, 2, 1, 1, 1, 0, 10, 5, 3, 2, 3, 2, 2, 1, 1, 1, 0, 12, 6, 4, 2, 3, 3, 2, 2, 1, 1, 1, 0, 15, 7, 6, 3, 3, 4, 3, 2, 2, 1, 1, 1, 0, 18, 9, 6, 4, 3, 4, 4, 3, 2, 2, 1, 1, 1
Offset: 0
Examples
Triangle begins: 1; 0, 1; 0, 1, 1; 0, 2, 1, 1; 0, 2, 1, 1, 1; 0, 3, 1, 1, 1, 1; 0, 4, 2, 2, 1, 1, 1; 0, 5, 3, 1, 2, 1, 1, 1; 0, 6, 3, 1, 2, 2, 1, 1, 1; 0, 8, 4, 3, 2, 2, 2, 1, 1, 1; 0, 10, 5, 3, 2, 3, 2, 2, 1, 1, 1; 0, 12, 6, 4, 2, 3, 3, 2, 2, 1, 1, 1; 0, 15, 7, 6, 3, 3, 4, 3, 2, 2, 1, 1, 1; 0, 18, 9, 6, 4, 3, 4, 4, 3, 2, 2, 1, 1, 1;
Crossrefs
Formula
For k > 0, g.f. of column k: Sum_{i>=0} x^(k*i) * Product_{j=1..k*i-1} (1+x^j).