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%I #10 Apr 07 2024 17:43:39
%S 1,3,21,164,1353,11508,99808,877425,7790745,69704921,627438606,
%T 5675535000,51546958296,469764721533,4293594852225,39341599326304,
%U 361271345551257,3323924166943410,30634431485945569,282767849049333909,2613630939017216898
%N a(n) = Sum_{k=0..floor(n/3)} (-1)^k * binomial(4*n-3*k-1,n-3*k).
%F a(n) = [x^n] 1/((1+x^3) * (1-x)^(3*n)).
%F a(n) = binomial(4*n-1, n)*hypergeom([1, (1-n)/3, (2-n)/3, -n/3], [(1-4*n)/3, (2-4*n)/3, 1-4*n/3], -1). - _Stefano Spezia_, Apr 07 2024
%o (PARI) a(n) = sum(k=0, n\3, (-1)^k*binomial(4*n-3*k-1, n-3*k));
%Y Cf. A120305, A262977, A371816.
%Y Cf. A371771.
%K nonn
%O 0,2
%A _Seiichi Manyama_, Apr 06 2024
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