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%I #10 May 01 2024 09:01:04
%S 1,2,10,62,402,2662,17914,122040,839154,5811758,40482530,283311470,
%T 1990464450,14030571258,99179197512,702789627712,4990636603986,
%U 35506061422530,253030893941362,1805893735209486,12906043894108162,92346511605008562,661494201448139850
%N Coefficient of x^n in the expansion of 1 / (1-x-x^3)^(2*n).
%F a(n) = Sum_{k=0..floor(n/3)} binomial(2*n+k-1,k) * binomial(3*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-x^3)^2 ). See A368962.
%o (PARI) a(n, s=3, t=2, u=0) = 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. A368962.
%K nonn
%O 0,2
%A _Seiichi Manyama_, May 01 2024
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