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 A384324 #17 May 27 2025 10:10:25
%S A384324 1,6,33,200,1428,12408,132604,1730160,27043866,495026316,10388326986,
%T A384324 245555445888,6446710871724,185904786328920,5836500883321164,
%U A384324 198054400887909264,7220679972923312487,281402128806812402490,11671796413017231008663
%N A384324 Expansion of Product_{k>=1} 1/(1 - k*x)^((2/3)^k).
%F A384324 G.f. A(x) satisfies A(x) = A(x/(1-x))^(2/3) / (1-x)^2.
%F A384324 G.f.: exp(3 * Sum_{k>=1} A004123(k+1) * x^k/k).
%F A384324 G.f.: B(x)^6, where B(x) is the g.f. of A090351.
%F A384324 a(n) ~ (n-1)! / log(3/2)^(n+1). - _Vaclav Kotesovec_, May 27 2025
%t A384324 terms = 20; A[_] = 1; Do[A[x_] = -2*A[x] + 3*A[x/(1-x)]^(2/3) / (1-x)^2 + O[x]^j // Normal, {j, 1, terms}]; CoefficientList[A[x], x] (* _Vaclav Kotesovec_, May 27 2025 *)
%o A384324 (PARI) my(N=20, x='x+O('x^N)); Vec(exp(3*sum(k=1, N, sum(j=0, k, 2^j*j!*stirling(k, j, 2))*x^k/k)))
%Y A384324 Cf. A084785, A384305, A384325, A384326.
%Y A384324 Cf. A004123, A090351, A090352.
%K A384324 nonn
%O A384324 0,2
%A A384324 _Seiichi Manyama_, May 26 2025