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 A333153 #6 Mar 09 2020 10:48:47
%S A333153 0,0,1,1,1,1,3,3,5,5,7,7,12,12,17,20,25,28,36,39,51,57,69,79,98,108,
%T A333153 131,148,175,196,235,260,307,344,400,450,522,581,671,751,859,957,1097,
%U A333153 1218,1385,1543,1744,1940,2193,2428,2735,3033,3400,3763,4215,4654
%N A333153 G.f.: Sum_{k>=1} (k * x^(k*(k+1)) / Product_{j=1..k} (1 - x^j)).
%H A333153 Vaclav Kotesovec, <a href="/A333153/b333153.txt">Table of n, a(n) for n = 0..10000</a>
%F A333153 a(n) ~ c * exp(2*Pi*sqrt(n/15)) / n^(1/4), where c = A333155 / (2 * 3^(1/4) * 5^(1/2) * phi^(1/2)) = 0.07923971705837122678006319599762... and phi = A001622 = (1+sqrt(5))/2 is the golden ratio.
%p A333153 b:= proc(n, i) option remember; `if`(n=0, 1,
%p A333153 `if`(i<1, 0, b(n, i-1)+`if`(i>n, 0, b(n-i, i))))
%p A333153 end:
%p A333153 a:= n-> add(k * b(n-k*(k+1), k), k=1..floor(sqrt(n))):
%p A333153 seq(a(n), n=0..60); # after _Alois P. Heinz_
%t A333153 nmax = 60; CoefficientList[Series[Sum[n * x^(n*(n+1)) / Product[1 - x^k, {k, 1, n}], {n, 0, Sqrt[nmax]}], {x, 0, nmax}], x]
%Y A333153 Cf. A003106, A268188, A333154.
%K A333153 nonn
%O A333153 0,7
%A A333153 _Vaclav Kotesovec_, Mar 09 2020