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 A344067 #9 May 09 2021 03:34:00
%S A344067 1,1,8,72,576,5120,41472,364544,2949120,25952256,209977344,1830813696,
%T A344067 14931722240,129251672064,1053340729344,9123584278528,74294344286208,
%U A344067 639503450505216,5239722662166528,44846880273727488,367008185258606592,3144110674230116352,25718087147075928064
%N A344067 Expansion of Product_{k>=1} (1 + 8^(k-1)*x^k).
%F A344067 a(n) = Sum_{k=0..A003056(n)} q(n,k) * 8^(n-k), where q(n,k) is the number of partitions of n into k distinct parts.
%F A344067 a(n) ~ (-polylog(2, -1/8))^(1/4) * 8^n * exp(2*sqrt(-polylog(2, -1/8)*n)) / (6*sqrt(Pi/8)*n^(3/4)). - _Vaclav Kotesovec_, May 09 2021
%t A344067 nmax = 22; CoefficientList[Series[Product[(1 + 8^(k - 1) x^k), {k, 1, nmax}], {x, 0, nmax}], x]
%t A344067 Table[Sum[Length[Select[IntegerPartitions[n, {k}], UnsameQ @@ # &]] 8^(n - k), {k, 0, Floor[(Sqrt[8 n + 1] - 1)/2]}], {n, 0, 22}]
%o A344067 (PARI) seq(n)={Vec(prod(k=1, n, 1 + 8^(k-1)*x^k + O(x*x^n)))} \\ _Andrew Howroyd_, May 08 2021
%Y A344067 Cf. A003056, A008289, A304961, A338677, A340103, A344062, A344063, A344064, A344065, A344066, A344068.
%K A344067 nonn
%O A344067 0,3
%A A344067 _Ilya Gutkovskiy_, May 08 2021