A363778 Square array T(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of 1/(Sum_{j>=0} x^(j^2))^k.

1, 1, 0, 1, -1, 0, 1, -2, 1, 0, 1, -3, 3, -1, 0, 1, -4, 6, -4, 0, 0, 1, -5, 10, -10, 3, 1, 0, 1, -6, 15, -20, 12, 0, -2, 0, 1, -7, 21, -35, 31, -9, -5, 3, 0, 1, -8, 28, -56, 65, -36, -2, 12, -3, 0, 1, -9, 36, -84, 120, -96, 24, 24, -18, 1, 0, 1, -10, 45, -120, 203, -210, 105, 20, -54, 18, 2, 0

Offset: 0

Author

Seiichi Manyama, Jun 21 2023

Keywords

• sign
• tabl

Examples

			Square array begins:
  1,  1,  1,   1,   1,   1,    1, ...
  0, -1, -2,  -3,  -4,  -5,   -6, ...
  0,  1,  3,   6,  10,  15,   21, ...
  0, -1, -4, -10, -20, -35,  -56, ...
  0,  0,  3,  12,  31,  65,  120, ...
  0,  1,  0,  -9, -36, -96, -210, ...
  0, -2, -5,  -2,  24, 105,  294, ...
		

Crossrefs

Columns k=0..3 give A000007, A317665, A363774, A363775.

Main diagonal gives A363780.

Cf. A045847, A162552, A363779.

Formula

T(0,k) = 1; T(n,k) = -(k/n) * Sum_{j=1..n} A162552(j) * T(n-j,k).