A293386 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/(1 + Sum_{j=1..k} j*x^(j*i))^2.

1, 1, 0, 1, -2, 0, 1, -2, 1, 0, 1, -2, -3, -2, 0, 1, -2, -3, 10, 4, 0, 1, -2, -3, 4, -4, -4, 0, 1, -2, -3, 4, 14, -20, 5, 0, 1, -2, -3, 4, 6, -8, 41, -6, 0, 1, -2, -3, 4, 6, 16, -46, 2, 9, 0, 1, -2, -3, 4, 6, 6, -30, 14, -111, -12, 0, 1, -2, -3, 4, 6, 6, 0, -58

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,  1,  -3, -3, -3, ...
   0, -2,  10,  4,  4, ...
   0,  4,  -4, 14,  6, ...
   0, -4, -20, -8, 16, ...

Crossrefs

Columns k=0..1 give A000007, A022597.

Rows n=0 gives A000012.

Main diagonal gives A252650.

Product_{i>0} (1 + Sum_{j=1..k} j*x^(j*i))^m: this sequence (m=-2), A290217 (m=-1), A290216 (m=1), A293377 (m=2).

Sequence in context: A275760 A293388 A268833 * A322522 A168121 A158948

Adjacent sequences: A293383 A293384 A293385 * A293387 A293388 A293389

Keyword

sign,tabl

Author

Seiichi Manyama, Oct 07 2017

Status

approved