A290216 Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of g.f. Product_{i>0} (1 + Sum_{j=1..k} j*x^(j*i)).

1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 3, 2, 0, 1, 1, 3, 2, 2, 0, 1, 1, 3, 5, 6, 3, 0, 1, 1, 3, 5, 6, 7, 4, 0, 1, 1, 3, 5, 10, 10, 12, 5, 0, 1, 1, 3, 5, 10, 10, 18, 13, 6, 0, 1, 1, 3, 5, 10, 15, 22, 25, 22, 8, 0, 1, 1, 3, 5, 10, 15, 22, 29, 34, 26, 10, 0, 1, 1, 3, 5

Offset: 0

Author

Seiichi Manyama, Oct 06 2017

Keywords

• nonn
• tabl

Examples

			Square array begins:
   1, 1, 1,  1,  1, ...
   0, 1, 1,  1,  1, ...
   0, 1, 3,  3,  3, ...
   0, 2, 2,  5,  5, ...
   0, 2, 6,  6, 10, ...
   0, 3, 7, 10, 10, ...
		

Links

• Seiichi Manyama, Antidiagonals n = 0..139, flattened

Crossrefs

Columns k=0..3 give A000007, A000009, A293204, A290269.

Rows n=0 gives A000012.

Main diagonal gives A077285.

Product_{i>0} (1 + Sum_{j=1..k} j*x^(j*i))^m: A290217 (m=-1), this sequence (m=1), A293377 (m=2).

Cf. A293305.