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A369983
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Maximum of the absolute value of the coefficients of (1 - x)^3 * (1 - x^2)^3 * (1 - x^3)^3 * ... * (1 - x^n)^3.
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1
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1, 3, 8, 15, 44, 50, 117, 186, 356, 561, 972, 1761, 3508, 5789, 10470, 19023, 35580, 62388, 113418, 205653, 376496, 674085, 1226181, 2211462, 4056220, 7287672, 13261764, 24005627, 43800562, 79033269, 143513301, 260061408, 473603594, 855436899, 1553736558, 2813222766
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OFFSET
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0,2
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LINKS
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MATHEMATICA
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Table[Max[Abs[CoefficientList[Product[(1 - x^k)^3, {k, 1, n}], x]]], {n, 0, 35}]
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PROG
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(PARI) a(n) = vecmax(apply(abs, Vec(prod(i=1, n, (1-x^i)^3)))); \\ Michel Marcus, Feb 07 2024
(Python)
from collections import Counter
c = {0:1}
for k in range(1, n+1):
d = Counter(c)
for j in c:
a = c[j]
d[j+k] -= 3*a
d[j+2*k] += 3*a
d[j+3*k] -= a
c = d
return max(map(abs, c.values())) # Chai Wah Wu, Feb 07 2024
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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