A350504 - OEIS

%I #29 Mar 01 2022 07:25:18

%S 1,1,1,1,2,2,3,5,8,13,22,38,68,118,211,380,692,1262,2316,4277,7930,

%T 14745,27517,51541,96792,182182,343711,650095,1231932,2338706,4447510,

%U 8472697,16164914,30884150,59086618,113189168,217091832,416839177,801247614,1541726967,2969432270

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

%H Seiichi Manyama, <a href="/A350504/b350504.txt">Table of n, a(n) for n = 0..1000</a>

%F a(n) ~ sqrt(3) * 2^(n - 1/2) / (sqrt(Pi) * n^(3/2)). - _Vaclav Kotesovec_, Feb 04 2022

%p b:= proc(n) option remember; `if`(n=0, 1,

%p       expand((1+x^(2*n-1))*b(n-1)))

%p     end:

%p a:= n-> max(coeffs(b(n))):

%p seq(a(n), n=0..40);  # _Alois P. Heinz_, Jan 28 2022

%t b[n_] := b[n] = If[n == 0, 1, Expand[(1 + x^(2*n - 1))*b[n - 1]]];

%t a[n_] := Max[CoefficientList[b[n], x]];

%t Table[a[n], {n, 0, 40}] (* _Jean-François Alcover_, Mar 01 2022, after _Alois P. Heinz_ *)

%o (PARI) a(n) = vecmax(Vec(prod(k=1, n, 1+x^(2*k-1)))); \\ _Seiichi Manyama_, Jan 28 2021

%Y Cf. A025591, A039828, A160235, A350457.

%K nonn

%O 0,5

%A _Ilya Gutkovskiy_, Jan 28 2022