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 A338677 #13 May 09 2021 02:27:03
%S A338677 1,1,9,73,649,5257,46729,378505,3331721,27219593,237491849,1938544265,
%T A338677 16925054601,138041874057,1196384310921,9820024329865,84609648809609,
%U A338677 693596417152649,5977550934234761,48976660041553545,419984680697190025,3455551232025810569,29494747047731910281
%N A338677 Expansion of Product_{k>=1} 1 / (1 - 8^(k-1)*x^k).
%F A338677 a(n) = Sum_{k=0..n} p(n,k) * 8^(n-k), where p(n,k) = number of partitions of n into k parts.
%F A338677 a(n) ~ sqrt(7) * polylog(2, 1/8)^(1/4) * 8^(n - 1/2) * exp(2*sqrt(polylog(2, 1/8)*n)) / (2*sqrt(Pi)*n^(3/4)). - _Vaclav Kotesovec_, May 09 2021
%t A338677 nmax = 22; CoefficientList[Series[Product[1/(1 - 8^(k - 1) x^k), {k, 1, nmax}], {x, 0, nmax}], x]
%t A338677 Table[Sum[Length[IntegerPartitions[n, {k}]] 8^(n - k), {k, 0, n}], {n, 0, 22}]
%t A338677 a[n_] := a[n] = If[n == 0, 1, (1/n) Sum[Sum[d 8^(k - k/d), {d, Divisors[k]}] a[n - k], {k, 1, n}]]; Table[a[n], {n, 0, 22}]
%Y A338677 Cf. A008284, A075900, A246940, A300579, A338673, A338674, A338675, A338676, A338678, A338679.
%K A338677 nonn
%O A338677 0,3
%A A338677 _Ilya Gutkovskiy_, Apr 23 2021