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 A344064 #9 May 09 2021 03:32:53
%S A344064 1,1,5,30,150,875,4500,25625,131250,750000,3843750,21562500,112109375,
%T A344064 621093750,3222656250,17880859375,92578125000,508300781250,
%U A344064 2658691406250,14465332031250,75439453125000,411254882812500,2142486572265625,11590576171875000,60722351074218750,326728820800781250
%N A344064 Expansion of Product_{k>=1} (1 + 5^(k-1)*x^k).
%F A344064 a(n) = Sum_{k=0..A003056(n)} q(n,k) * 5^(n-k), where q(n,k) is the number of partitions of n into k distinct parts.
%F A344064 a(n) ~ (-polylog(2, -1/5))^(1/4) * 5^n * exp(2*sqrt(-polylog(2, -1/5)*n)) / (2*sqrt(6*Pi/5)*n^(3/4)). - _Vaclav Kotesovec_, May 09 2021
%t A344064 nmax = 25; CoefficientList[Series[Product[(1 + 5^(k - 1) x^k), {k, 1, nmax}], {x, 0, nmax}], x]
%t A344064 Table[Sum[Length[Select[IntegerPartitions[n, {k}], UnsameQ @@ # &]] 5^(n - k), {k, 0, Floor[(Sqrt[8 n + 1] - 1)/2]}], {n, 0, 25}]
%o A344064 (PARI) seq(n)={Vec(prod(k=1, n, 1 + 5^(k-1)*x^k + O(x*x^n)))} \\ _Andrew Howroyd_, May 08 2021
%Y A344064 Cf. A003056, A008289, A261569, A304961, A338674, A340103, A344062, A344063, A344065, A344066, A344067, A344068.
%K A344064 nonn
%O A344064 0,3
%A A344064 _Ilya Gutkovskiy_, May 08 2021