%I #11 Feb 26 2023 06:56:03
%S 1,1,3,7,22,76,290,1225,5616,27758,147050,829926,4966258,31382572,
%T 208676004,1455540594,10620614461,80869622604,641177678068,
%U 5282866462839,45152445030267,399673570426188,3658433105500600,34582526451125235,337165886689229224
%N G.f. satisfies A(x) = 1 + x * (1 + x)^2 * A(x * (1 + x)).
%H Seiichi Manyama, <a href="/A360887/b360887.txt">Table of n, a(n) for n = 0..577</a>
%F a(0) = 1; a(n) = Sum_{k=0..n-1} binomial(n+1-k,k) * a(n-1-k).
%o (PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=0, i-1, binomial(i+1-j, j)*v[i-j])); v;
%Y Cf. A360888, A360889.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Feb 25 2023