A382974 Square array A(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where A(n,k) = [x^n * y^k] Product_{j>=1} 1/(1 - x^j + y^j).

1, -1, 1, 0, -2, 2, -1, 2, -4, 3, 1, -3, 4, -7, 5, -1, 4, -8, 10, -12, 7, 1, -5, 14, -20, 18, -19, 11, -1, 6, -18, 34, -40, 34, -30, 15, 2, -7, 22, -51, 78, -77, 56, -45, 22, -2, 9, -30, 75, -127, 157, -139, 94, -67, 30, 2, -11, 42, -105, 196, -282, 306, -239, 146, -97, 42

Offset

0,5

Links

Table of n, a(n) for n=0..65.

Example

Square array begins:
   1,  -1,  0,   -1,   1,   -1,    1, ...
   1,  -2,  2,   -3,   4,   -5,    6, ...
   2,  -4,  4,   -8,  14,  -18,   22, ...
   3,  -7, 10,  -20,  34,  -51,   75, ...
   5, -12, 18,  -40,  78, -127,  196, ...
   7, -19, 34,  -77, 157, -282,  478, ...
  11, -30, 56, -139, 306, -582, 1048, ...

Crossrefs

Columns k=0..1 give A000041, (-1)*A000070.

Rows n=0..1 give A081362, (-1)^k * A304631(k).

Main diagonal gives A382979.

Antidiagonal sums give A000007.

Cf. A322210.

Sequence in context: A353368 A300667 A129687 * A274742 A128176 A368415

Adjacent sequences: A382971 A382972 A382973 * A382975 A382976 A382977

Keyword

sign,tabl

Author

Seiichi Manyama, Apr 11 2025

Status

approved