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 A384343 #14 May 29 2025 07:16:19
%S A384343 1,1,-1,3,-14,86,-650,5822,-60287,708873,-9334633,136142011,
%T A384343 -2179136696,37987580268,-716513806824,14540745561432,
%U A384343 -315936103907094,7318039354370826,-180020739049731594,4687207255550122014,-128782014195949550724,3723598212075752653284,-113023054997369519314572
%N A384343 Expansion of Product_{k>=1} (1 + k*x)^((1/2)^(k+1)).
%F A384343 G.f. A(x) satisfies A(x) = (1+x)^(1/2) * A(x/(1+x))^(1/2).
%F A384343 G.f.: exp(Sum_{k>=1} (-1)^(k-1) * A000670(k) * x^k/k).
%F A384343 G.f.: 1/B(-x), where B(x) is the g.f. of A084784.
%F A384343 a(n) ~ (-1)^(n+1) * (n-1)! / (2*log(2)^(n+1)). - _Vaclav Kotesovec_, May 29 2025
%t A384343 terms = 25; A[_] = 1; Do[A[x_] = -A[x] + 2*((1 + x)*A[x/(1 + x)])^(1/2) + O[x]^j // Normal, {j, 1, terms}]; CoefficientList[A[x], x] (* _Vaclav Kotesovec_, May 29 2025 *)
%o A384343 (PARI) my(N=30, x='x+O('x^N)); Vec(exp(sum(k=1, N, (-1)^(k-1)*sum(j=0, k, j!*stirling(k, j, 2))*x^k/k)))
%Y A384343 Cf. A381890, A384344, A384345.
%Y A384343 Cf. A000670, A084784.
%K A384343 sign
%O A384343 0,4
%A A384343 _Seiichi Manyama_, May 26 2025