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 A305105 #15 Jan 21 2025 09:03:13
%S A305105 0,1,3,8,17,34,64,114,195,325,526,832,1292,1970,2958,4384,6413,9276,
%T A305105 13283,18836,26478,36924,51096,70210,95844,130019,175350,235192,
%U A305105 313802,416618,550540,724250,948719,1237732,1608508,2082600,2686857,3454590,4427144,5655652
%N A305105 G.f.: Sum_{k>=1} x^(2*k-1)/(1-x^(2*k-1)) * Product_{k>=1} (1+x^k)/(1-x^k).
%C A305105 Convolution of A066897 and A000009.
%C A305105 Convolution of A067588 and A000041.
%C A305105 Let A(x) = Sum_{k >= 1} x^(2*k-1)/(1 - x^(2*k-1)) * Product_{k >= 1} (1 + x^k)/(1 - x^k). Then A(x) = Sum_{k >= 1} x^(2*k-1)/(1 - x^(2*k-1)) * Product_{k >= 1} (1 + x^k)/(1 + x^k - 2*x^k) == Sum_{k >= 1} x^(2*k-1)/(1 - x^(2*k-1)) (mod 2). It follows from the comment in A001227 by _Juri-Stepan Gerasimov_, dated Jul 17 2016, that a(n) is odd iff n is a square or twice a square. - _Peter Bala_, Jan 10 2025
%H A305105 Vaclav Kotesovec, <a href="/A305105/b305105.txt">Table of n, a(n) for n = 0..10000</a>
%F A305105 a(n) ~ (2*gamma + log(16*n/Pi^2)) * exp(Pi*sqrt(n)) / (16*Pi*sqrt(n)), where gamma is the Euler-Mascheroni constant A001620.
%t A305105 nmax = 50; CoefficientList[Series[Sum[x^(2*k-1)/(1-x^(2*k-1)), {k, 1, nmax}] * Product[(1+x^k)/(1-x^k), {k, 1, nmax}], {x, 0, nmax}], x]
%Y A305105 Cf. A001227, A015128, A066897, A067588, A305102, A305104.
%K A305105 nonn,easy
%O A305105 0,3
%A A305105 _Vaclav Kotesovec_, May 25 2018