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 A306734 #15 Mar 11 2020 09:51:18
%S A306734 1,1,1,0,1,1,1,1,0,1,1,1,2,1,1,1,1,1,1,2,2,2,2,2,1,2,2,1,2,2,3,3,3,3,
%T A306734 3,3,3,3,2,3,3,3,4,4,4,5,5,5,5,5,5,5,5,4,5,5,6,6,6,7,7,8,8,8,9,9,8,9,
%U A306734 8,8,9,9,9,9,10,10,11,12,12,13,13,14,15,14,15,15,15,15,15,15,16
%N A306734 Expansion of Sum_{k>=0} x^(k^2) * Product_{j=1..k} (1 + x^j).
%H A306734 Vaclav Kotesovec, <a href="/A306734/b306734.txt">Table of n, a(n) for n = 0..10000</a>
%F A306734 a(n) ~ c * A333198^sqrt(n) / sqrt(n), where c = 0.424889520435345887204307524... = sqrt((23 + (10051/2 - (1173*sqrt(69))/2)^(1/3) + ((23/2)*(437 + 51*sqrt(69)))^(1/3))/69)/2, c = sqrt(s)/2, where s is the real root of the equation -1 + 6*s - 23*s^2 + 23*s^3 = 0. - _Vaclav Kotesovec_, Mar 11 2020
%F A306734 Limit_{n->infinity} a(n) / A333179(n) = A060006 = (1/2 + sqrt(23/3)/6)^(1/3) + (1/2 - sqrt(23/3)/6)^(1/3) = 1.32471795724474602596090885... - _Vaclav Kotesovec_, Mar 11 2020
%t A306734 nmax = 90; CoefficientList[Series[Sum[x^(k^2) Product[(1 + x^j), {j, 1, k}], {k, 0, nmax}], {x, 0, nmax}], x]
%t A306734 nmax = 100; p = 1; s = 1; Do[p = Expand[p*(1 + x^k)*x^(2*k - 1)]; p = Take[p, Min[nmax + 1, Exponent[p, x] + 1, Length[p]]]; s += p;, {k, 1, Sqrt[nmax]}]; Take[CoefficientList[s, x], nmax + 1] (* _Vaclav Kotesovec_, Mar 10 2020 *)
%Y A306734 Cf. A003114, A053256, A053258, A053261, A333179, A333180.
%K A306734 nonn
%O A306734 0,13
%A A306734 _Ilya Gutkovskiy_, Mar 06 2019