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%I #12 Feb 11 2024 09:16:39
%S 1,4,28,226,1940,17214,155914,1432106,13289076,124276528,1169346298,
%T 11057293526,104986087178,1000248093420,9557756114130,91559051752596,
%U 879027678226452,8455595252761536,81476137225450096,786286875175380088,7598503022428758570
%N Coefficient of x^n in the expansion of ( (1+x)^2 * (1+x+x^3)^2 )^n.
%F a(n) = Sum_{k=0..floor(n/3)} binomial(2*n,k) * binomial(4*n-k,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)^2 * (1+x+x^3)^2) ). See A369485.
%o (PARI) a(n, s=3, t=2, u=2) = sum(k=0, n\s, binomial(t*n, k)*binomial((t+u)*n-k, n-s*k));
%Y Cf. A370185, A370186.
%Y Cf. A369485.
%K nonn
%O 0,2
%A _Seiichi Manyama_, Feb 11 2024