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 A384334 #15 May 27 2025 10:10:40
%S A384334 1,20,110,340,-1995,53904,-1534600,49159600,-1758057650,69662897000,
%T A384334 -3037327435860,144787947993000,-7502235351828450,420296374337607600,
%U A384334 -25335189019626256200,1636008982452733508400,-112721505676611504401025,8256863266451569604835900
%N A384334 Expansion of Product_{k>=1} (1 + k*x)^((4/5)^k).
%F A384334 G.f. A(x) satisfies A(x) = (1+x)^4 * A(x/(1+x))^(4/5).
%F A384334 G.f.: exp(5 * Sum_{k>=1} (-1)^(k-1) * A094417(k) * x^k/k).
%F A384334 G.f.: 1/B(-x), where B(x) is the g.f. of A384326.
%F A384334 G.f.: B(x)^20, where B(x) is the g.f. of A384345.
%F A384334 a(n) ~ (-1)^(n+1) * (n-1)! / log(5/4)^(n+1). - _Vaclav Kotesovec_, May 27 2025
%t A384334 terms = 20; A[_] = 1; Do[A[x_] = -4*A[x] + 5*A[x/(1+x)]^(4/5) * (1+x)^4 + O[x]^j // Normal, {j, 1, terms}]; CoefficientList[A[x], x] (* _Vaclav Kotesovec_, May 27 2025 *)
%o A384334 (PARI) my(N=20, x='x+O('x^N)); Vec(exp(5*sum(k=1, N, (-1)^(k-1)*sum(j=0, k, 4^j*j!*stirling(k, j, 2))*x^k/k)))
%Y A384334 Cf. A116603, A384332, A384333.
%Y A384334 Cf. A094417, A384326, A384345.
%K A384334 sign
%O A384334 0,2
%A A384334 _Seiichi Manyama_, May 26 2025