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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..20.

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}]

CROSSREFS

Cf. A010815, A008705, A252654, A252782, A255672, A270917, A270922, A281266, A281267, A281268, A283333, A292805, A300456, A300458.

Sequence in context: A217472 A156654 A098815 * A289329 A033464 A170924

Adjacent sequences:  A300454 A300455 A300456 * A300458 A300459 A300460

KEYWORD

sign

AUTHOR

Ilya Gutkovskiy, Mar 06 2018

STATUS

approved

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Last modified April 3 03:14 EDT 2020. Contains 333195 sequences. (Running on oeis4.)