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%I #9 Apr 05 2024 13:06:19
%S 1,3,15,85,505,3081,19125,120173,761995,4865697,31244029,201544551,
%T 1305039209,8477521051,55221311565,360559717807,2359123470971,
%U 15463951609491,101530816122729,667587477393509,4395294402200983,28972295880583861,191181607835416543
%N a(n) = Sum_{k=0..floor(n/3)} binomial(3*n-2*k,n-3*k).
%F a(n) = [x^n] 1/((1-x-x^3) * (1-x)^(2*n)).
%F a(n) ~ 3^(3*n + 5/2) / (17 * sqrt(Pi*n) * 2^(2*n)). - _Vaclav Kotesovec_, Apr 05 2024
%o (PARI) a(n) = sum(k=0, n\3, binomial(3*n-2*k, n-3*k));
%Y Cf. A144904, A371755, A371756.
%Y Cf. A066380, A371742.
%K nonn
%O 0,2
%A _Seiichi Manyama_, Apr 05 2024
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