The OEIS is supported by the many generous donors to the OEIS Foundation.
%I #9 Jan 05 2023 15:04:16
%S 1,2,4,13,57,315,2057,15484,132317,1261560,13281295,153218597,
%T 1921565205,26008169266,377922606876,5871153031163,97096594212804,
%U 1702487540383101,31551431772637772,616331122530164638
%N Largest coefficient in expansion of Product (1+q^1+q^3...+q^(2i-1)), i=1 to n.
%H Vaclav Kotesovec, <a href="/A039831/b039831.txt">Table of n, a(n) for n = 1..400</a>
%F Conjecture: a(n) ~ 3 * n^n / exp(n). - _Vaclav Kotesovec_, Jan 05 2023
%t Table[Max[CoefficientList[Expand[Product[1 + Sum[x^(2*k-1), {k, 1, j}], {j, 1, n}]], x]], {n,1,20}] (* _Vaclav Kotesovec_, Jan 05 2023 *)
%Y Cf. A039824.
%K nonn
%O 1,2
%A _Olivier Gérard_