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%I #13 Jun 18 2022 14:00:20
%S 1,1,4,43,1279,108472,26888677,19761575473,43356335678176,
%T 284807217244068223,5608422162798704960959,
%U 331227791701602557410058404,58679652813856265804094312228601,31185477505022553490008128886444268657
%N G.f. A(x) satisfies A(x) = 1 + x * A(3 * x / (1 - x)) / (1 - x).
%F a(0) = 1; a(n) = Sum_{k=0..n-1} 3^k * binomial(n-1,k) * a(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, 3^j*binomial(i-1, j)*v[j+1])); v;
%Y Column k=3 of A306245.
%Y Cf. A000110, A126443, A355082.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Jun 18 2022
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