This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A305123 #13 Jan 14 2025 03:16:52
%S A305123 0,1,0,3,2,7,6,15,16,32,36,62,74,117,142,214,264,377,468,648,806,1090,
%T A305123 1354,1791,2224,2894,3580,4598,5670,7193,8838,11102,13588,16925,20632,
%U A305123 25501,30972,38021,46000,56135,67668,82119,98642,119115,142592,171412,204520
%N A305123 G.f.: Sum_{k>=1} x^(2*k-1)/(1+x^(2*k-1)) * Product_{k>=1} 1/(1-x^k).
%C A305123 Conjecture: a(n) is odd iff n is a term of A067567. - _Peter Bala_, Jan 10 2025
%H A305123 Vaclav Kotesovec, <a href="/A305123/b305123.txt">Table of n, a(n) for n = 0..10000</a>
%F A305123 For n > 0, a(n) = A209423(n) - A305121(n).
%F A305123 a(n) ~ log(2) * exp(Pi*sqrt(2*n/3)) / (2^(5/2)*Pi*sqrt(n)).
%t A305123 nmax = 60; CoefficientList[Series[Sum[x^(2*k-1)/(1+x^(2*k-1)), {k, 1, nmax}] * Product[1/(1-x^k), {k, 1, nmax}], {x, 0, nmax}], x]
%Y A305123 Cf. A000041, A001227, A006128, A067567, A209423, A066898, A305121, A066897.
%Y A305123 Cf. A116676, A305124.
%K A305123 nonn
%O A305123 0,4
%A A305123 _Vaclav Kotesovec_, May 26 2018