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 A023019 #31 Jun 28 2025 08:46:21
%S A023019 1,21,252,2233,16170,100926,560945,2837418,13266099,57994475,
%T A023019 239170239,937026279,3507380170,12601619226,43628951025,146036139347,
%U A023019 473924014599,1494785958435,4591920193357,13764656869425,40328218603134
%N A023019 Number of partitions of n into parts of 21 kinds.
%C A023019 a(n) is the Euler transform of A010860. - _Alois P. Heinz_, Oct 17 2008
%H A023019 Seiichi Manyama, <a href="/A023019/b023019.txt">Table of n, a(n) for n = 0..1000</a>
%H A023019 N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%H A023019 <a href="/index/Pro#1mxtok">Index entries for expansions of Product_{k >= 1} (1-x^k)^m</a>
%F A023019 a(0) = 1, a(n) = (21/n)*Sum_{k=1..n} A000203(k)*a(n-k) for n > 0. - _Seiichi Manyama_, Mar 27 2017
%F A023019 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 = 21. - _Vaclav Kotesovec_, Jun 28 2025
%p A023019 with (numtheory): a:= proc(n) option remember; `if`(n=0, 1, add (add (d*21, d=divisors(j)) *a(n-j), j=1..n)/n) end: seq (a(n), n=0..40); # _Alois P. Heinz_, Oct 17 2008
%t A023019 CoefficientList[Series[1/QPochhammer[x]^21, {x, 0, 30}], x] (* _Indranil Ghosh_, Mar 27 2017 *)
%o A023019 (PARI) Vec(1/eta(x)^21 + O(x^30)) \\ _Indranil Ghosh_, Mar 27 2017
%Y A023019 Cf. 21st column of A144064. - _Alois P. Heinz_, Oct 17 2008
%K A023019 nonn
%O A023019 0,2
%A A023019 _David W. Wilson_, Jun 14 1998