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A300457
a(n) = [x^n] Product_{k=1..n} (1 - x^k)^(n^k).
2
1, -1, -3, -1, 25, 624, 9871, 170470, 3027249, 55077245, 979330606, 15079702923, 94670678245, -7958168036625, -626145997536240, -34564907982551791, -1733699815491494303, -84294315853736719077, -4067859614343931897505, -196552300464314521511610, -9519733465269825759734169
OFFSET
0,3
EXAMPLE
The table of coefficients of x^k in expansion of Product_{k>=1} (1 - x^k)^(n^k) begins:
n = 0: (1), 0, 0, 0, 0, 0, ...
n = 1: 1, (-1), -1, 0, 0, 1, ...
n = 2: 1, -2, (-3), 0, 2, 12, ...
n = 3: 1, -3, -6, (-1), 9, 63, ...
n = 4: 1, -4, -10, -4, (25), 224, ...
n = 5: 1, -5, -15, -10, 55, (624), ...
MATHEMATICA
Table[SeriesCoefficient[Product[(1 - x^k)^(n^k), {k, 1, n}], {x, 0, n}], {n, 0, 20}]
KEYWORD
sign
AUTHOR
Ilya Gutkovskiy, Mar 06 2018
STATUS
approved