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%I #5 Mar 06 2018 17:50:46
%S 1,-1,-3,-1,25,624,9871,170470,3027249,55077245,979330606,15079702923,
%T 94670678245,-7958168036625,-626145997536240,-34564907982551791,
%U -1733699815491494303,-84294315853736719077,-4067859614343931897505,-196552300464314521511610,-9519733465269825759734169
%N a(n) = [x^n] Product_{k=1..n} (1 - x^k)^(n^k).
%e The table of coefficients of x^k in expansion of Product_{k>=1} (1 - x^k)^(n^k) begins:
%e n = 0: (1), 0, 0, 0, 0, 0, ...
%e n = 1: 1, (-1), -1, 0, 0, 1, ...
%e n = 2: 1, -2, (-3), 0, 2, 12, ...
%e n = 3: 1, -3, -6, (-1), 9, 63, ...
%e n = 4: 1, -4, -10, -4, (25), 224, ...
%e n = 5: 1, -5, -15, -10, 55, (624), ...
%t Table[SeriesCoefficient[Product[(1 - x^k)^(n^k), {k, 1, n}], {x, 0, n}], {n, 0, 20}]
%Y Cf. A010815, A008705, A252654, A252782, A255672, A270917, A270922, A281266, A281267, A281268, A283333, A292805, A300456, A300458.
%K sign
%O 0,3
%A _Ilya Gutkovskiy_, Mar 06 2018
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