A371657 - OEIS

%I #23 Dec 25 2024 05:33:57

%S 1,3,27,333,4752,73764,1209492,20610693,361403937,6478386561,

%T 118181952369,2186908154748,40949739595242,774474351098031,

%U 14772979729013247,283878381945510621,5490264493926636912,106786725176131118523,2087502569999563971843

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

%H Seiichi Manyama, <a href="/A371657/b371657.txt">Table of n, a(n) for n = 0..756</a>

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

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

%Y Cf. A107708, A156016.

%Y Cf. A219534, A219537, A371658.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Apr 01 2024