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 A377154 #42 Oct 31 2024 11:23:21
%S A377154 1,1,7,43,385,3721,47911,612067,9559873,157478545,2910837511,
%T A377154 56866891291,1224263236417,27618866777113,673173639519655,
%U A377154 17237263465417171,469017851840595841,13367670808113197857,401964392506370969863,12604372518766870306315,414278024498330114803201
%N A377154 Expansion of e.g.f. exp(Sum_{k>=1} A000082(k)*x^k/k).
%H A377154 Vaclav Kotesovec, <a href="/A377154/b377154.txt">Table of n, a(n) for n = 0..428</a>
%F A377154 a(n) ~ n! * 5^(1/6) * exp(-1/12 - 1/(20*Pi^2) - 3^(2/3)*n^(1/3) / (10^(1/3)*Pi^(4/3)) + 3^(4/3)*5^(1/3)*n^(2/3) / (2*Pi)^(2/3)) / (6^(1/3) * Pi^(5/6) * n^(2/3)).
%F A377154 a(n) ~ 10^(1/6) * exp(-1/12 - 1/(20*Pi^2) - 3^(2/3)*n^(1/3) / (10^(1/3)*Pi^(4/3)) + 3^(4/3)*5^(1/3)*n^(2/3) / (2*Pi)^(2/3)) * n^(n - 1/6) / (3^(1/3) * Pi^(1/3) * exp(n)).
%F A377154 E.g.f.: exp(Sum_{k>=1} A001615(k)*x^k).
%t A377154 nmax = 25; CoefficientList[Series[Exp[Sum[k * Product[1 + 1/p, {p, Select[Divisors[k], PrimeQ]}] * x^k, {k, 1, nmax}]], {x, 0, nmax}], x] * Range[0, nmax]!
%Y A377154 Cf. A000082, A001615, A308462.
%K A377154 nonn
%O A377154 0,3
%A A377154 _Vaclav Kotesovec_, Oct 31 2024