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%I #8 Oct 03 2023 09:00:21
%S 1,4,20,145,1250,11746,116641,1204039,12790067,138895021,1535005454,
%T 17207743738,195197256289,2236419124408,25842382083071,
%U 300822398531482,3524358836945936,41524956284752018,491722951928324392,5848997420625891294,69854562522309219081
%N G.f. A(x) satisfies A(x) = 1/(1 - x)^3 + x*A(x)^3/(1 - x)^2.
%F a(n) = Sum_{k=0..n} binomial(n+7*k+2,n-k) * binomial(3*k,k)/(2*k+1).
%o (PARI) a(n) = sum(k=0, n, binomial(n+7*k+2, n-k)*binomial(3*k, k)/(2*k+1));
%Y Cf. A364623, A366182, A366184.
%K nonn
%O 0,2
%A _Seiichi Manyama_, Oct 03 2023