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 A385543 #13 Jul 03 2025 15:01:59
%S A385543 1,1,2,7,49,676,18861,1062533,121557594,28281916427,13399862563765,
%T A385543 12949857822909156,25549330363139585961,103025771800413460066681,
%U A385543 849971455496325163128172498,14359775106466928789344919850719,497276944869002836686738999984515113
%N A385543 G.f. A(x) satisfies A(x) = Sum_{k>=0} x^k * A(k^2*x).
%F A385543 a(0) = 1; a(n) = Sum_{k=0..n-1} (n-k)^(2*k) * a(k).
%F A385543 From _Vaclav Kotesovec_, Jul 03 2025: (Start)
%F A385543 a(n) ~ c * n! * 3^(n*(n-4)/3) / 2^(n/3), where
%F A385543 c = 438919.4178887847632978930903514036169636302175176... if mod(n,3) = 0,
%F A385543 c = 438919.4215235929223401081041169940935227575106084... if mod(n,3) = 1,
%F A385543 c = 438919.4025215529290127441106624079221416448856280... if mod(n,3) = 2. (End)
%t A385543 a[0] = 1; a[n_] := a[n] = Sum[(n-k)^(2*k) * a[k], {k, 0, n-1}]; Table[a[n], {n, 0, 20}] (* _Vaclav Kotesovec_, Jul 03 2025 *)
%o A385543 (PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=0, i-1, (i-j)^(2*j)*v[j+1])); v;
%Y A385543 Cf. A125282, A385547.
%K A385543 nonn,easy
%O A385543 0,3
%A A385543 _Seiichi Manyama_, Jul 03 2025