%I #10 Aug 27 2023 04:39:06

%S 1,1,4,24,169,1301,10605,89963,785943,7023148,63892489,589771350,

%T 5509967214,52001860377,495048989686,4748144843341,45838627944500,

%U 445072967642096,4343508043479012,42581707009501604,419158119684986781,4141270208611084284

%N G.f. satisfies A(x) = 1 + x*A(x)^5 / (1 + x*A(x)^2).

%F a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(2*n+3*k+1,k) * binomial(n-1,n-k)/(2*n+3*k+1).

%o (PARI) a(n) = sum(k=0, n, (-1)^(n-k)*binomial(2*n+3*k+1, k)*binomial(n-1, n-k)/(2*n+3*k+1));

%Y Cf. A002293, A271469, A349361, A364759, A364866, A365226.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Aug 27 2023