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 A384305 #29 May 31 2025 04:10:25
%S A384305 1,30,615,11260,205695,4013406,88035585,2255192280,68859250020,
%T A384305 2506898720040,107238427737876,5281094776037040,293625956135692020,
%U A384305 18139856902224931080,1229886945212115522060,90641666662687182976896,7206758883035555464430370,614391718014749017022916060
%N A384305 Expansion of Product_{k>=1} 1/(1 - k*x)^((5/6)^k).
%F A384305 G.f. A(x) satisfies A(x) = A(x/(1-x))^(5/6) / (1-x)^5.
%F A384305 G.f.: exp(6 * Sum_{k>=1} A094418(k) * x^k/k).
%F A384305 G.f.: B(x)^30, where B(x) is the g.f. of A090358.
%F A384305 a(n) ~ (n-1)! / log(6/5)^(n+1). - _Vaclav Kotesovec_, May 31 2025
%t A384305 terms = 20; A[_] = 1; Do[A[x_] = -5*A[x] + 6*A[x/(1-x)]^(5/6) / (1-x)^5 + O[x]^j // Normal, {j, 1, terms}]; CoefficientList[A[x], x] (* _Vaclav Kotesovec_, May 31 2025 *)
%o A384305 (PARI) my(N=20, x='x+O('x^N)); Vec(exp(6*sum(k=1, N, sum(j=0, k, 5^j*j!*stirling(k, j, 2))*x^k/k)))
%Y A384305 Cf. A084785, A384324, A384325, A384326.
%Y A384305 Cf. A090358, A090362, A094418.
%K A384305 nonn
%O A384305 0,2
%A A384305 _Seiichi Manyama_, May 26 2025