A300457
a(n) = [x^n] Product_{k=1..n} (1 - x^k)^(n^k).
Original entry on oeis.org
1, -1, -3, -1, 25, 624, 9871, 170470, 3027249, 55077245, 979330606, 15079702923, 94670678245, -7958168036625, -626145997536240, -34564907982551791, -1733699815491494303, -84294315853736719077, -4067859614343931897505, -196552300464314521511610, -9519733465269825759734169
Offset: 0
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), ...
Cf.
A010815,
A008705,
A252654,
A252782,
A255672,
A270917,
A270922,
A281266,
A281267,
A281268,
A283333,
A292805,
A300456,
A300458.
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Table[SeriesCoefficient[Product[(1 - x^k)^(n^k), {k, 1, n}], {x, 0, n}], {n, 0, 20}]
A300458
a(n) = [x^n] Product_{k=1..n} 1/(1 + x^k)^(n^k).
Original entry on oeis.org
1, -1, -1, -10, 11, 374, 9792, 183847, 3469427, 65038049, 1195396233, 19667738452, 189089161562, -6219720781782, -606316892131934, -35104997710496175, -1795953382595105853, -88223902016631657740, -4283800987347611165184, -207864171877269042498096, -10102590396625592962089500
Offset: 0
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), ...
Cf.
A081362,
A252654,
A255526,
A252782,
A255672,
A270917,
A270922,
A281266,
A281267,
A281268,
A283333,
A292805,
A300456,
A300457.
-
Table[SeriesCoefficient[Product[1/(1 + x^k)^(n^k), {k, 1, n}], {x, 0, n}], {n, 0, 20}]
Showing 1-2 of 2 results.