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 A377509 #11 Oct 31 2024 11:23:16
%S A377509 1,1,2,36,234,7290,54540,1408680,23119740,341788860,11790437400,
%T A377509 231972879600,8206299070200,191673262380600,6154270418696400,
%U A377509 206515993375692000,6574758436640394000,269828090984990538000,9531096165082736244000,411037724983993923816000
%N A377509 Expansion of e.g.f. exp(Sum_{k>=1} phi(k)^4 * x^k/k), where phi is the Euler totient function A000010.
%H A377509 Vaclav Kotesovec, <a href="/A377509/b377509.txt">Table of n, a(n) for n = 0..412</a>
%F A377509 log(a(n)/n!) ~ 5 * 3^(1/5) * c^(1/5) * n^(4/5) / 2^(7/5), where c = Product_{primes p} (1 - 4/p^2 + 6/p^3 - 4/p^4 + 1/p^5) = 0.286256471511560891173288340086638647956...
%t A377509 nmax = 25; $RecursionLimit->Infinity; a[n_]:=a[n]=If[n==0, 1, Sum[EulerPhi[k]^4 * a[n-k], {k, 1, n}]/n];Table[a[n]*n!, {n, 0, nmax}]
%t A377509 nmax = 25; CoefficientList[Series[Exp[Sum[EulerPhi[k]^4 * x^k / k, {k, 1, nmax}]], {x, 0, nmax}], x] * Range[0, nmax]!
%Y A377509 Cf. A318917, A377507, A377508.
%Y A377509 Cf. A205797, A361148.
%K A377509 nonn
%O A377509 0,3
%A A377509 _Vaclav Kotesovec_, Oct 30 2024