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 A023016 #26 Jun 28 2025 08:45:00
%S A023016 1,18,189,1482,9576,53676,269325,1235286,5256711,20985272,79260723,
%T A023016 285139764,982349361,3255488082,10416507579,32281134120,97154549289,
%U A023016 284625019800,813310723925,2270826800172,6204926551824,16615751700618
%N A023016 Number of partitions of n into parts of 18 kinds.
%C A023016 a(n) is Euler transform of A010857. - _Alois P. Heinz_, Oct 17 2008
%H A023016 Seiichi Manyama, <a href="/A023016/b023016.txt">Table of n, a(n) for n = 0..1000</a>
%H A023016 <a href="/index/Pro#1mxtok">Index entries for expansions of Product_{k >= 1} (1-x^k)^m</a>
%F A023016 a(0) = 1, a(n) = (18/n)*Sum_{k=1..n} A000203(k)*a(n-k) for n > 0. - _Seiichi Manyama_, Mar 27 2017
%F A023016 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 = 18. - _Vaclav Kotesovec_, Jun 28 2025
%p A023016 with(numtheory): a:= proc(n) option remember; `if`(n=0, 1, add(add(d*18, d=divisors(j)) *a(n-j), j=1..n)/n) end: seq(a(n), n=0..40); # _Alois P. Heinz_, Oct 17 2008
%t A023016 CoefficientList[Series[1/QPochhammer[x]^18, {x, 0, 30}], x] (* _Indranil Ghosh_, Mar 27 2017 *)
%o A023016 (PARI) Vec(1/eta(x)^18 + O(x^30)) \\ _Indranil Ghosh_, Mar 27 2017
%Y A023016 Cf. 18th column of A144064. - _Alois P. Heinz_, Oct 17 2008
%K A023016 nonn
%O A023016 0,2
%A A023016 _David W. Wilson_