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A350504
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Maximal coefficient of (1 + x) * (1 + x^3) * (1 + x^5) * ... * (1 + x^(2*n-1)).
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1
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1, 1, 1, 1, 2, 2, 3, 5, 8, 13, 22, 38, 68, 118, 211, 380, 692, 1262, 2316, 4277, 7930, 14745, 27517, 51541, 96792, 182182, 343711, 650095, 1231932, 2338706, 4447510, 8472697, 16164914, 30884150, 59086618, 113189168, 217091832, 416839177, 801247614, 1541726967, 2969432270
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OFFSET
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0,5
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LINKS
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FORMULA
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a(n) ~ sqrt(3) * 2^(n - 1/2) / (sqrt(Pi) * n^(3/2)). - Vaclav Kotesovec, Feb 04 2022
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MAPLE
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b:= proc(n) option remember; `if`(n=0, 1,
expand((1+x^(2*n-1))*b(n-1)))
end:
a:= n-> max(coeffs(b(n))):
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MATHEMATICA
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b[n_] := b[n] = If[n == 0, 1, Expand[(1 + x^(2*n - 1))*b[n - 1]]];
a[n_] := Max[CoefficientList[b[n], x]];
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PROG
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(PARI) a(n) = vecmax(Vec(prod(k=1, n, 1+x^(2*k-1)))); \\ Seiichi Manyama, Jan 28 2021
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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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