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 A384333 #14 May 27 2025 10:10:37
%S A384333 1,12,30,76,-819,15120,-320568,7719984,-208986462,6300545128,
%T A384333 -209806494828,7660698340008,-304718887446110,13127557400200944,
%U A384333 -609336227455254936,30330991088734345200,-1612305658103085757467,91179423240593288760396,-5467060640706775435713298
%N A384333 Expansion of Product_{k>=1} (1 + k*x)^((3/4)^k).
%F A384333 G.f. A(x) satisfies A(x) = (1+x)^3 * A(x/(1+x))^(3/4).
%F A384333 G.f.: exp(4 * Sum_{k>=1} (-1)^(k-1) * A032033(k) * x^k/k).
%F A384333 G.f.: 1/B(-x), where B(x) is the g.f. of A384325.
%F A384333 G.f.: B(x)^12, where B(x) is the g.f. of A381890.
%F A384333 a(n) ~ (-1)^(n+1) * (n-1)! / log(4/3)^(n+1). - _Vaclav Kotesovec_, May 27 2025
%t A384333 terms = 20; A[_] = 1; Do[A[x_] = -3*A[x] + 4*A[x/(1+x)]^(3/4) * (1+x)^3 + O[x]^j // Normal, {j, 1, terms}]; CoefficientList[A[x], x] (* _Vaclav Kotesovec_, May 27 2025 *)
%o A384333 (PARI) my(N=20, x='x+O('x^N)); Vec(exp(4*sum(k=1, N, (-1)^(k-1)*sum(j=0, k, 3^j*j!*stirling(k, j, 2))*x^k/k)))
%Y A384333 Cf. A116603, A384332, A384334.
%Y A384333 Cf. A032033, A381890, A384325.
%K A384333 sign
%O A384333 0,2
%A A384333 _Seiichi Manyama_, May 26 2025