|
%I #4 Mar 06 2018 17:50:52
%S 1,-1,-1,-10,11,374,9792,183847,3469427,65038049,1195396233,
%T 19667738452,189089161562,-6219720781782,-606316892131934,
%U -35104997710496175,-1795953382595105853,-88223902016631657740,-4283800987347611165184,-207864171877269042498096,-10102590396625592962089500
%N a(n) = [x^n] Product_{k=1..n} 1/(1 + x^k)^(n^k).
%e The table of coefficients of x^k in expansion of Product_{k>=1} 1/(1 + x^k)^(n^k) begins:
%e n = 0: (1), 0, 0, 0, 0, 0, ...
%e n = 1: 1, (-1), 0, -1, 1, -1, ...
%e n = 2: 1, -2, (-1), -4, 3, -2, ...
%e n = 3: 1, -3, -3, (-10), 6, 15, ...
%e n = 4: 1, -4, -6, -20, (11), 104, ...
%e n = 5: 1, -5, -10, -35, 20, (374), ...
%t Table[SeriesCoefficient[Product[1/(1 + x^k)^(n^k), {k, 1, n}], {x, 0, n}], {n, 0, 20}]
%Y Cf. A081362, A252654, A255526, A252782, A255672, A270917, A270922, A281266, A281267, A281268, A283333, A292805, A300456, A300457.
%K sign
%O 0,4
%A _Ilya Gutkovskiy_, Mar 06 2018
|
