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%I #11 Nov 03 2023 11:18:28
%S 1,1,5,27,177,1270,9645,76206,619913,5156959,43667985,375140383,
%T 3261467573,28641957520,253702185717,2263964868768,20334261430769,
%U 183680693283325,1667613040080061,15208587941854251,139266058402655669,1279953660931370623
%N G.f. satisfies A(x) = 1 + x*A(x)^4 + x^2*A(x).
%F a(n) = Sum_{k=0..floor(n/2)} binomial(3*n-5*k+1,k) * binomial(4*n-7*k,n-2*k)/(3*n-5*k+1).
%o (PARI) a(n) = sum(k=0, n\2, binomial(3*n-5*k+1, k)*binomial(4*n-7*k, n-2*k)/(3*n-5*k+1));
%Y Cf. A365178, A365180, A365181, A365182, A365183, A367041, A367049, A367050.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Nov 03 2023
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