%I #10 Jun 18 2022 14:00:28

%S 1,1,5,89,5949,1546225,1591006901,6526287232201,106972340665773165,

%T 7011394913950382306529,1838058207026378316690626149,

%U 1927362102757461997768349891040825,8083963777926072174628168609626454270621

%N G.f. A(x) satisfies A(x) = 1 + x * A(4 * x / (1 - x)) / (1 - x).

%F a(0) = 1; a(n) = Sum_{k=0..n-1} 4^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, 4^j*binomial(i-1, j)*v[j+1])); v;

%Y Column k=4 of A306245.

%Y Cf. A000110, A126443, A355081.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Jun 18 2022