A283272 Square array A(n,k), n>=0, k>=0, read by antidiagonals, where column k is expansion of Product_{j>=1} (1-x^j)^(j^k) in power of x.

1, 1, -1, 1, -1, -1, 1, -1, -2, 0, 1, -1, -4, -1, 0, 1, -1, -8, -5, 0, 1, 1, -1, -16, -19, -1, 4, 0, 1, -1, -32, -65, -9, 21, 4, 1, 1, -1, -64, -211, -55, 127, 49, 7, 0, 1, -1, -128, -665, -285, 807, 500, 81, 3, 0, 1, -1, -256, -2059, -1351, 5179, 4809, 1038, 45

Offset

0,9

Links

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

Formula

G.f. of column k: Product_{j>=1} (1-x^j)^(j^k).

Example

Square array begins:
   1,  1,  1,   1,   1,    1, ...
  -1, -1, -1,  -1,  -1,   -1, ...
  -1, -2, -4,  -8, -16,  -32, ...
   0, -1, -5, -19, -65, -211, ...
   0,  0, -1,  -9, -55, -285, ...
   1,  4, 21, 127, 807, 5179, ...

Crossrefs

Columns k=0-9 give A010815, A073592, A283263, A283264, A283271, A283336, A283337, A283338, A283339, A283340.

Row k=5 gives A281581.

Main diagonal gives A283333.

Cf. A144048.

Sequence in context: A110298 A362379 A144740 * A292166 A282192 A049501

Adjacent sequences: A283269 A283270 A283271 * A283273 A283274 A283275

Keyword

sign,tabl

Author

Seiichi Manyama, Mar 04 2017

Status

approved