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%I #16 Mar 30 2024 01:41:30
%S 1,1,3,15,82,495,3147,20812,141621,985287,6976369,50108232,364202415,
%T 2673756449,19797659586,147677816532,1108711280376,8371222635096,
%U 63525564996093,484243596619753,3706268752629237,28470703720193010,219432896755734137
%N G.f. satisfies A(x) = 1 + x / (1 - x*A(x)^3)^3.
%H Seiichi Manyama, <a href="/A371616/b371616.txt">Table of n, a(n) for n = 0..1000</a>
%F a(n) = Sum_{k=0..n} binomial(3*(n-k)+1,k) * binomial(n+2*k-1,n-k)/(3*(n-k)+1).
%o (PARI) a(n, r=1, s=3, t=0, u=3) = r*sum(k=0, n, binomial(t*k+u*(n-k)+r, k)*binomial(n+(s-1)*k-1, n-k)/(t*k+u*(n-k)+r));
%Y Cf. A364742, A367242.
%Y Cf. A001764, A365113.
%Y Cf. A002293, A367281.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Mar 29 2024
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