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 A305201 #13 Dec 04 2024 16:10:04
%S A305201 1,1,5,26,208,1644,18728,201466,2809672,39505800,647509992,
%T A305201 10851033984,210456343392,4090234000800,89123794754304,
%U A305201 2000019423403824,48674645933985408,1217362548455301504,32913123947574009984,910006995701419453440,26898048642355515339264
%N A305201 Expansion of e.g.f. Product_{k>=1} 1/(1 - H(k)*x^k), where H(k) is the k-th harmonic number.
%H A305201 Vaclav Kotesovec, <a href="/A305201/b305201.txt">Table of n, a(n) for n = 0..430</a>
%H A305201 Vaclav Kotesovec, <a href="/A305201/a305201.jpg">Graph - the asymptotic ratio (5000 terms)</a>
%F A305201 E.g.f.: Product_{k>=1} 1/(1 - (A001008(k)/A002805(k))*x^k).
%F A305201 E.g.f.: exp(Sum_{k>=1} Sum_{j>=1} H(j)^k*x^(j*k)/k).
%F A305201 a(n) ~ n! * c * (3/2)^(n/2 + 1) / (3 - sqrt(6)), where c = Product_{k>=3} 1/(1 - (2/3)^(k/2) * H(k)) = 20723937.5142714953478411012151498609843924051679047516... - _Vaclav Kotesovec_, Nov 05 2019
%t A305201 nmax = 20; CoefficientList[Series[Product[1/(1 - HarmonicNumber[k] x^k), {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]!
%t A305201 nmax = 20; CoefficientList[Series[Exp[Sum[Sum[HarmonicNumber[j]^k x^(j k)/k, {j, 1, nmax}], {k, 1, nmax}]], {x, 0, nmax}], x] Range[0, nmax]!
%t A305201 a[n_] := a[n] = If[n == 0, 1, Sum[Sum[d HarmonicNumber[d]^(k/d), {d, Divisors[k]}] a[n - k], {k, 1, n}]/n]; Table[n! a[n], {n, 0, 20}]
%Y A305201 Cf. A001008, A002805, A007841, A303970, A305203.
%K A305201 nonn
%O A305201 0,3
%A A305201 _Ilya Gutkovskiy_, May 27 2018