A300458 a(n) = [x^n] Product_{k=1..n} 1/(1 + x^k)^(n^k).

1, -1, -1, -10, 11, 374, 9792, 183847, 3469427, 65038049, 1195396233, 19667738452, 189089161562, -6219720781782, -606316892131934, -35104997710496175, -1795953382595105853, -88223902016631657740, -4283800987347611165184, -207864171877269042498096, -10102590396625592962089500

Offset: 0

Author

Ilya Gutkovskiy, Mar 06 2018

Keywords

• sign

Examples

			The table of coefficients of x^k in expansion of Product_{k>=1} 1/(1 + x^k)^(n^k) begins:
n = 0: (1),  0,    0,    0,   0,     0,  ...
n = 1:  1, (-1),   0,   -1,   1,    -1,  ...
n = 2:  1,  -2,  (-1),  -4,   3,    -2,  ...
n = 3:  1,  -3,   -3, (-10),  6,    15,  ...
n = 4:  1,  -4,   -6,  -20, (11),  104,  ...
n = 5:  1,  -5,  -10,  -35,  20,  (374), ...
		

Crossrefs

Cf. A081362, A252654, A255526, A252782, A255672, A270917, A270922, A281266, A281267, A281268, A283333, A292805, A300456, A300457.

Programs

Mathematica

Table[SeriesCoefficient[Product[1/(1 + x^k)^(n^k), {k, 1, n}], {x, 0, n}], {n, 0, 20}]