A364758 - OEIS

%I #8 Aug 06 2023 11:04:31

%S 1,1,3,14,76,450,2818,18352,123028,843345,5884227,41650479,298352365,

%T 2158751879,15754446893,115830820439,857147952469,6379136387303,

%U 47715901304501,358529599468636,2704884469806606,20481615947325089,155605509972859999

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

%F a(n) = (1/n) * Sum_{k=0..n-1} (-1)^k * binomial(n,k) * binomial(4*n-3*k,n-1-k) for n > 0.

%o (PARI) a(n) = if(n==0, 1, sum(k=0, n-1, (-1)^k*binomial(n, k)*binomial(4*n-3*k, n-1-k))/n);

%Y Cf. A090192, A106228, A364759.

%Y Cf. A364747.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Aug 05 2023