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%I #6 Feb 14 2024 10:47:55
%S 1,3,17,102,645,4193,27764,186231,1261213,8604759,59053167,407217396,
%T 2819252544,19583729766,136426565999,952743556907,6667916884701,
%U 46755146944959,328398159653117,2310073990369926,16271915501598595,114757849228310355
%N Coefficient of x^n in the expansion of ( (1+x)^3 + x^2 )^n.
%F a(n) = Sum_{k=0..floor(n/2)} binomial(n,k) * binomial(3*n-3*k,n-2*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)^3 + x^2) ).
%o (PARI) a(n) = sum(k=0, n\2, binomial(n, k)*binomial(3*n-3*k, n-2*k));
%Y Cf. A002426, A006139.
%Y Cf. A188686, A370287.
%Y Cf. A065065.
%K nonn
%O 0,2
%A _Seiichi Manyama_, Feb 14 2024
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