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 A384325 #14 May 27 2025 07:56:56
%S A384325 1,12,114,1084,11319,136920,1981228,34705656,731268315,18203860748,
%T A384325 524073230394,17111173850652,623571696107069,25046605210733184,
%U A384325 1097919954149781264,52109508350206511840,2660615337817983390318,145353541761618312219336
%N A384325 Expansion of Product_{k>=1} 1/(1 - k*x)^((3/4)^k).
%F A384325 G.f. A(x) satisfies A(x) = A(x/(1-x))^(3/4) / (1-x)^3.
%F A384325 G.f.: exp(4 * Sum_{k>=1} A032033(k) * x^k/k).
%F A384325 G.f.: B(x)^12, where B(x) is the g.f. of A090353.
%F A384325 a(n) ~ (n-1)! / log(4/3)^(n+1). - _Vaclav Kotesovec_, May 27 2025
%t A384325 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 A384325 (PARI) my(N=20, x='x+O('x^N)); Vec(exp(4*sum(k=1, N, sum(j=0, k, 3^j*j!*stirling(k, j, 2))*x^k/k)))
%Y A384325 Cf. A084785, A384305, A384324, A384326.
%Y A384325 Cf. A032033, A090353.
%K A384325 nonn
%O A384325 0,2
%A A384325 _Seiichi Manyama_, May 26 2025