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%I #11 Apr 30 2024 06:08:11
%S 1,0,0,3,4,5,21,49,92,237,595,1331,3169,7787,18487,44108,107036,
%T 258349,622371,1508239,3658679,8869465,21543005,52399612,127497281,
%U 310487855,756858661,1846060464,4505442967,11003284052,26887642756,65735882819,160795695676
%N Coefficient of x^n in the expansion of ( (1-x+x^3) / (1-x) )^n.
%F a(n) = Sum_{k=0..floor(n/3)} binomial(n,k) * binomial(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) ).
%o (PARI) a(n, s=3, t=1, u=1) = sum(k=0, n\s, binomial(t*n, k)*binomial((u-t+1)*n-(s-1)*k-1, n-s*k));
%Y Cf. A372414, A372415.
%Y Cf. A114997.
%K nonn
%O 0,4
%A _Seiichi Manyama_, Apr 29 2024
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