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A385585 G.f. A(x) satisfies A(x) = Sum_{k>=0} (k*x)^k * A(k*x).

%I A385585 #10 Jul 04 2025 04:45:21
%S A385585 1,1,5,40,457,7101,148270,4206121,165267951,9117777074,709325010385,
%T A385585 77906424970811,12109278363587036,2670187179684919761,
%U A385585 836451775445907622685,372646977140600929476104,236390047765997660237447061,213719117789650238860723125601
%N A385585 G.f. A(x) satisfies A(x) = Sum_{k>=0} (k*x)^k * A(k*x).
%F A385585 a(0) = 1; a(n) = Sum_{k=0..n-1} (n-k)^n * a(k).
%F A385585 From _Vaclav Kotesovec_, Jul 04 2025: (Start)
%F A385585 a(n) ~ c * 3^(n*(n+3)/6), where
%F A385585 c = 14331.87392277329... if mod(n,3) = 0,
%F A385585 c = 14331.87383811849... if mod(n,3) = 1,
%F A385585 c = 14331.87405112061... if mod(n,3) = 2. (End)
%t A385585 a[0] = 1; a[n_] := a[n] = Sum[(n-k)^n * a[k], {k, 0, n-1}]; Table[a[n], {n, 0, 20}] (* _Vaclav Kotesovec_, Jul 04 2025 *)
%o A385585 (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)^i*v[j+1])); v;
%Y A385585 Cf. A125282, A385544.
%Y A385585 Cf. A218683.
%K A385585 nonn
%O A385585 0,3
%A A385585 _Seiichi Manyama_, Jul 03 2025