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%I A372373 #9 Apr 29 2024 09:28:58
%S A372373 1,1,1,10,37,91,334,1366,4645,15967,59951,220782,792946,2906554,
%T A372373 10770082,39629440,145966549,540943231,2006762563,7443051014,
%U A372373 27661527427,102980882455,383639407570,1430429881122,5339465251426,19947662875216,74573064834646
%N A372373 Coefficient of x^n in the expansion of ( (1+x+x^3)^3 / (1+x)^2 )^n.
%F A372373 a(n) = Sum_{k=0..floor(n/3)} binomial(3*n,k) * binomial(n-k,n-3*k).
%F A372373 The g.f. exp( Sum_{k>=1} a(k) * x^k/k ) has integer coefficients and equals (1/x) * Series_Reversion( x * (1+x)^2 / (1+x+x^3)^3 ). See A372377.
%o A372373 (PARI) a(n, s=3, t=3, u=-2) = sum(k=0, n\s, binomial(t*n, k)*binomial((t+u)*n-k, n-s*k));
%Y A372373 Cf. A372372, A372374.
%Y A372373 Cf. A372377.
%K A372373 nonn
%O A372373 0,4
%A A372373 _Seiichi Manyama_, Apr 29 2024

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