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 A338697 #19 May 09 2021 05:44:02
%S A338697 1,1,3,13,101,931,12391,178809,3331721,66288142,1589753211,
%T A338697 40104031166,1183380156013,36187564837217,1262524447510383,
%U A338697 45533370885563716,1834219414937219601,76016894083755947753,3479900167920331954531,162982921698852088968886,8341707623665223127224821
%N A338697 a(n) = [x^n] Product_{k>=1} 1 / (1 - n^(k-1)*x^k).
%H A338697 Vaclav Kotesovec, <a href="/A338697/b338697.txt">Table of n, a(n) for n = 0..385</a>
%F A338697 a(n) = Sum_{k=0..n} p(n,k) * n^(n-k), where p(n,k) is the number of partitions of n into k parts.
%F A338697 a(n) ~ c * n^(n-1), where c = BesselI(1,2) = A096789 = 1.590636854637329... - _Vaclav Kotesovec_, May 09 2021
%t A338697 Table[SeriesCoefficient[Product[1/(1 - n^(k - 1) x^k), {k, 1, n}], {x, 0, n}], {n, 0, 20}]
%t A338697 Join[{1}, Table[Sum[Length[IntegerPartitions[n, {k}]] n^(n - k), {k, 0, n}], {n, 1, 20}]]
%t A338697 Join[{1}, Table[SeriesCoefficient[x + (n-1)/(n*QPochhammer[1/n, n*x]), {x, 0, n}], {n, 1, 20}]] (* _Vaclav Kotesovec_, May 09 2021 *)
%Y A338697 Cf. A008284, A075900, A124577, A300579, A338673, A338674, A338675, A338676, A338677, A338678, A338679, A344095.
%K A338697 nonn
%O A338697 0,3
%A A338697 _Ilya Gutkovskiy_, Apr 24 2021