A293377 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))^2.

1, 1, 0, 1, 2, 0, 1, 2, 3, 0, 1, 2, 7, 6, 0, 1, 2, 7, 10, 9, 0, 1, 2, 7, 16, 25, 14, 0, 1, 2, 7, 16, 31, 38, 22, 0, 1, 2, 7, 16, 39, 62, 78, 32, 0, 1, 2, 7, 16, 39, 70, 117, 116, 46, 0, 1, 2, 7, 16, 39, 80, 149, 206, 206, 66, 0, 1, 2, 7, 16, 39, 80, 159, 262, 362

Offset

0,5

Links

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

Example

Square array begins:
   1,  1,  1,  1,  1, ...
   0,  2,  2,  2,  2, ...
   0,  3,  7,  7,  7, ...
   0,  6, 10, 16, 16, ...
   0,  9, 25, 31, 39, ...
   0, 14, 38, 62, 70, ...

Crossrefs

Columns k=0..1 give A000007, A022567.

Rows n=0 gives A000012.

Main diagonal gives A293378.

Product_{i>0} (1 + Sum_{j=1..k} j*x^(j*i))^m: A290217 (m=-1), A290216 (m=1), this sequence (m=2).

Sequence in context: A262881 A336820 A099173 * A159880 A289251 A353174

Adjacent sequences: A293374 A293375 A293376 * A293378 A293379 A293380

Keyword

nonn,tabl

Author

Seiichi Manyama, Oct 07 2017

Status

approved