A382975 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 + x^j - y^j).

1, -1, 1, -1, 0, 1, 0, -1, -1, 2, 0, -1, 0, -1, 2, 1, -1, -1, -1, -1, 3, 0, 0, 0, 0, -2, -2, 4, 1, 0, 0, -2, 0, -2, -2, 5, 0, 1, 0, -1, 0, -1, -2, -3, 6, 0, 1, 1, 0, -1, -1, -2, -3, -3, 8, 0, 1, 0, 0, -1, 2, -1, -2, -4, -5, 10, 0, 1, 1, 0, 1, -2, 0, -1, -2, -5, -5, 12

Offset

0,10

Links

Table of n, a(n) for n=0..77.

Example

Square array begins:
  1, -1, -1,  0,  0,  1,  0,  1, ...
  1,  0, -1, -1, -1,  0,  0,  1, ...
  1, -1,  0, -1,  0,  0,  0,  1, ...
  2, -1, -1,  0, -2, -1,  0,  0, ...
  2, -1, -2,  0,  0, -1, -1,  1, ...
  3, -2, -2, -1, -1,  2, -2,  0, ...
  4, -2, -2, -2, -1,  0,  0, -1, ...
  5, -3, -3, -2, -1,  0, -1,  4, ...

Crossrefs

Columns k=0..2 give A000009, (-1)*A025147, (-1)*A015744.

Rows n=0..2 give A010815, A078616, A297054.

Main diagonal gives A382980.

Antidiagonal sums give A000007.

Cf. A284593.

Sequence in context: A371074 A287104 A190483 * A090239 A165276 A035698

Adjacent sequences: A382972 A382973 A382974 * A382976 A382977 A382978

Keyword

sign,tabl

Author

Seiichi Manyama, Apr 11 2025

Status

approved