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 A023018 #25 Jun 28 2025 08:45:53
%S A023018 1,20,230,1960,13685,82524,443870,2175800,9869990,41907380,168012824,
%T A023018 640438680,2334121995,8171039800,27580783270,90058003200,285253928790,
%U A023018 878572253720,2636748302650,7725084195240,22130265931900,62079251390180
%N A023018 Number of partitions of n into parts of 20 kinds.
%C A023018 a(n) is Euler transform of A010859. - _Alois P. Heinz_, Oct 17 2008
%H A023018 Seiichi Manyama, <a href="/A023018/b023018.txt">Table of n, a(n) for n = 0..1000</a>
%H A023018 N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%H A023018 <a href="/index/Pro#1mxtok">Index entries for expansions of Product_{k >= 1} (1-x^k)^m</a>
%F A023018 G.f.: Product_{m>=1} 1/(1-x^m)^20.
%F A023018 a(0) = 1, a(n) = (20/n)*Sum_{k=1..n} A000203(k)*a(n-k) for n > 0. - _Seiichi Manyama_, Mar 27 2017
%F A023018 a(n) ~ m^((m+1)/4) * exp(Pi*sqrt(2*m*n/3)) / (2^((3*m+5)/4) * 3^((m+1)/4) * n^((m+3)/4)) * (1 - ((9+Pi^2)*m^2+36*m+27) / (24*Pi*sqrt(6*m*n))), set m = 20. - _Vaclav Kotesovec_, Jun 28 2025
%p A023018 with(numtheory): a:= proc(n) option remember; `if`(n=0, 1, add(add(d*20, d=divisors(j)) *a(n-j), j=1..n)/n) end: seq(a(n), n=0..40); # _Alois P. Heinz_, Oct 17 2008
%t A023018 CoefficientList[Series[1/QPochhammer[x]^20, {x, 0, 30}], x] (* _Indranil Ghosh_, Mar 27 2017 *)
%o A023018 (PARI) Vec(1/eta(x)^20 + O(x^30)) \\ _Indranil Ghosh_, Mar 27 2017
%Y A023018 20th column of A144064. - _Alois P. Heinz_, Oct 17 2008
%K A023018 nonn
%O A023018 0,2
%A A023018 _David W. Wilson_