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%I #11 Dec 30 2022 01:14:35
%S 1,2,4,8,16,32,72,176,384,976,2496,6560,17152,45952,123520,336640,
%T 920832,2526976,6979584,19379712,53966336,150892544,423132160,
%U 1190260736,3356964864,9491228672,26889519104,76351971328,217229369344,619159953408,1767696515072,5054679908352
%N Maximal coefficient of Product_{k=1..n} (1 + 2*x^k).
%H Vaclav Kotesovec, <a href="/A359389/b359389.txt">Table of n, a(n) for n = 0..1000</a>
%F a(n) ~ 3^(n + 3/2) / (2*sqrt(Pi)*n^(3/2)).
%t Table[Max[CoefficientList[Product[1 + 2*x^k, {k, 1, n}], x]], {n, 0, 40}]
%t p = 1; Join[{1}, Table[p = Expand[p*(1 + 2*x^n)]; Max[CoefficientList[p, x]], {n, 1, 40}]]
%o (PARI) a(n) = vecmax(Vec(prod(k=1, n, 1 + 2*x^k))); \\ _Michel Marcus_, Dec 29 2022
%Y Cf. A025591, A032302, A160235.
%K nonn
%O 0,2
%A _Vaclav Kotesovec_, Dec 29 2022
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