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 A023017 #26 Jun 28 2025 08:45:26
%S A023017 1,19,209,1710,11495,66880,347681,1649637,7252300,29875505,116319938,
%T A023017 430976031,1527928814,5206792965,17119704425,54484060983,168297474675,
%U A023017 505762373795,1481733152790,4239676354650,11866652524496,32536693623850
%N A023017 Number of partitions of n into parts of 19 kinds.
%C A023017 a(n) is Euler transform of A010858. - _Alois P. Heinz_, Oct 17 2008
%H A023017 Seiichi Manyama, <a href="/A023017/b023017.txt">Table of n, a(n) for n = 0..1000</a>
%H A023017 N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%H A023017 <a href="/index/Pro#1mxtok">Index entries for expansions of Product_{k >= 1} (1-x^k)^m</a>
%F A023017 a(0) = 1, a(n) = (19/n)*Sum_{k=1..n} A000203(k)*a(n-k) for n > 0. - _Seiichi Manyama_, Mar 27 2017
%F A023017 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 = 19. - _Vaclav Kotesovec_, Jun 28 2025
%p A023017 with(numtheory): a:= proc(n) option remember; `if`(n=0, 1, add(add(d*19, d=divisors(j)) *a(n-j), j=1..n)/n) end: seq(a(n), n=0..40); # _Alois P. Heinz_, Oct 17 2008
%t A023017 CoefficientList[Series[1/QPochhammer[x]^19, {x, 0, 30}], x] (* _Indranil Ghosh_, Mar 27 2017 *)
%o A023017 (PARI) Vec(1/eta(x)^19 + O(x^30)) \\ _Indranil Ghosh_, Mar 27 2017
%Y A023017 19th column of A144064. - _Alois P. Heinz_, Oct 17 2008
%K A023017 nonn
%O A023017 0,2
%A A023017 _David W. Wilson_