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 A377508 #10 Oct 31 2024 11:23:12
%S A377508 1,1,2,20,122,2122,15532,284104,3837500,52963964,1125315224,
%T A377508 20981180464,500475045688,10373180665720,264908485440848,
%U A377508 6624880728277088,185812008437953808,5449866267968244496,167510440639938875680,5447433174773217714496,177500241844579492474016
%N A377508 Expansion of e.g.f. exp(Sum_{k>=1} phi(k)^3 * x^k/k), where phi is the Euler totient function A000010.
%H A377508 Vaclav Kotesovec, <a href="/A377508/b377508.txt">Table of n, a(n) for n = 0..424</a>
%F A377508 log(a(n)/n!) ~ 2^(9/4) * c^(1/4) * n^(3/4) / 3^(3/4), where c = Product_{p primes} (1 - 3/p^2 + 3/p^3 - 1/p^4) = 0.337187873791589971961692816152158244949154127758...
%t A377508 nmax = 25; $RecursionLimit->Infinity; a[n_]:=a[n]=If[n==0, 1, Sum[EulerPhi[k]^3*a[n-k], {k, 1, n}]/n];Table[a[n]*n!, {n, 0, nmax}]
%t A377508 nmax = 25; CoefficientList[Series[Exp[Sum[EulerPhi[k]^3 * x^k / k, {k, 1, nmax}]], {x, 0, nmax}], x] * Range[0, nmax]!
%Y A377508 Cf. A318917, A377507, A377509.
%Y A377508 Cf. A178933, A358714.
%K A377508 nonn
%O A377508 0,3
%A A377508 _Vaclav Kotesovec_, Oct 30 2024