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 A384332 #15 May 27 2025 10:10:33
%S A384332 1,6,3,20,-207,2538,-36381,599760,-11210229,234779146,-5455240455,
%T A384332 139445920452,-3892724842549,117916363928070,-3854035833235839,
%U A384332 135241405277665656,-5072575747811807052,202559732310632082120,-8581116791103001216108
%N A384332 Expansion of Product_{k>=1} (1 + k*x)^((2/3)^k).
%F A384332 G.f. A(x) satisfies A(x) = (1+x)^2 * A(x/(1+x))^(2/3).
%F A384332 G.f.: exp(3 * Sum_{k>=1} (-1)^(k-1) * A004123(k+1) * x^k/k).
%F A384332 G.f.: 1/B(-x), where B(x) is the g.f. of A384324.
%F A384332 G.f.: B(x)^6, where B(x) is the g.f. of A384344.
%F A384332 a(n) ~ (-1)^(n+1) * (n-1)! / log(3/2)^(n+1). - _Vaclav Kotesovec_, May 27 2025
%t A384332 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 A384332 (PARI) my(N=20, x='x+O('x^N)); Vec(exp(3*sum(k=1, N, (-1)^(k-1)*sum(j=0, k, 2^j*j!*stirling(k, j, 2))*x^k/k)))
%Y A384332 Cf. A116603, A384333, A384334.
%Y A384332 Cf. A004123, A384324, A384344.
%K A384332 sign
%O A384332 0,2
%A A384332 _Seiichi Manyama_, May 26 2025