A366591 - OEIS

%I #11 Oct 14 2023 13:20:14

%S 1,0,0,1,2,1,3,12,18,24,75,180,295,620,1612,3365,6580,15365,35728,

%T 74906,163099,379242,848148,1848693,4187193,9583209,21417924,48067371,

%U 109877922,250010451,564688551,1286128272,2944963788,6714338592,15313680087,35108572386

%N G.f. A(x) satisfies A(x) = 1 + x^3*(1+x)^2*A(x)^3.

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

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

%Y Cf. A366221, A366590, A366592.

%Y Cf. A366555.

%K nonn

%O 0,5

%A _Seiichi Manyama_, Oct 14 2023