%I #6 May 02 2024 09:46:24

%S 1,3,21,171,1469,12988,116985,1067545,9836541,91313469,852701256,

%T 8001080244,75375985841,712487600698,6754115819535,64185511063246,

%U 611287650124125,5832863405199183,55750924705841643,533676328608473118,5115556211638071944

%N Coefficient of x^n in the expansion of 1 / ( (1-x) * (1-x-x^3)^2 )^n.

%F a(n) = Sum_{k=0..floor(n/3)} binomial(2*n+k-1,k) * binomial(4*n-2*k-1,n-3*k).

%F The g.f. exp( Sum_{k>=1} a(k) * x^k/k ) has integer coefficients and equals (1/x) * Series_Reversion( x * (1-x) * (1-x-x^3)^2 ). See A368966.

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

%Y Cf. A368966.

%K nonn

%O 0,2

%A _Seiichi Manyama_, May 01 2024