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A359389
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Maximal coefficient of Product_{k=1..n} (1 + 2*x^k).
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1
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1, 2, 4, 8, 16, 32, 72, 176, 384, 976, 2496, 6560, 17152, 45952, 123520, 336640, 920832, 2526976, 6979584, 19379712, 53966336, 150892544, 423132160, 1190260736, 3356964864, 9491228672, 26889519104, 76351971328, 217229369344, 619159953408, 1767696515072, 5054679908352
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OFFSET
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0,2
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LINKS
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FORMULA
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a(n) ~ 3^(n + 3/2) / (2*sqrt(Pi)*n^(3/2)).
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MATHEMATICA
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Table[Max[CoefficientList[Product[1 + 2*x^k, {k, 1, n}], x]], {n, 0, 40}]
p = 1; Join[{1}, Table[p = Expand[p*(1 + 2*x^n)]; Max[CoefficientList[p, x]], {n, 1, 40}]]
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PROG
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(PARI) a(n) = vecmax(Vec(prod(k=1, n, 1 + 2*x^k))); \\ Michel Marcus, Dec 29 2022
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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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