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A350504 Maximal coefficient of (1 + x) * (1 + x^3) * (1 + x^5) * ... * (1 + x^(2*n-1)).

%I A350504 #29 Mar 01 2022 07:25:18
%S A350504 1,1,1,1,2,2,3,5,8,13,22,38,68,118,211,380,692,1262,2316,4277,7930,
%T A350504 14745,27517,51541,96792,182182,343711,650095,1231932,2338706,4447510,
%U A350504 8472697,16164914,30884150,59086618,113189168,217091832,416839177,801247614,1541726967,2969432270
%N A350504 Maximal coefficient of (1 + x) * (1 + x^3) * (1 + x^5) * ... * (1 + x^(2*n-1)).
%H A350504 Seiichi Manyama, <a href="/A350504/b350504.txt">Table of n, a(n) for n = 0..1000</a>
%F A350504 a(n) ~ sqrt(3) * 2^(n - 1/2) / (sqrt(Pi) * n^(3/2)). - _Vaclav Kotesovec_, Feb 04 2022
%p A350504 b:= proc(n) option remember; `if`(n=0, 1,
%p A350504       expand((1+x^(2*n-1))*b(n-1)))
%p A350504     end:
%p A350504 a:= n-> max(coeffs(b(n))):
%p A350504 seq(a(n), n=0..40);  # _Alois P. Heinz_, Jan 28 2022
%t A350504 b[n_] := b[n] = If[n == 0, 1, Expand[(1 + x^(2*n - 1))*b[n - 1]]];
%t A350504 a[n_] := Max[CoefficientList[b[n], x]];
%t A350504 Table[a[n], {n, 0, 40}] (* _Jean-François Alcover_, Mar 01 2022, after _Alois P. Heinz_ *)
%o A350504 (PARI) a(n) = vecmax(Vec(prod(k=1, n, 1+x^(2*k-1)))); \\ _Seiichi Manyama_, Jan 28 2021
%Y A350504 Cf. A025591, A039828, A160235, A350457.
%K A350504 nonn
%O A350504 0,5
%A A350504 _Ilya Gutkovskiy_, Jan 28 2022