%I #9 Feb 14 2024 10:48:40

%S 1,3,27,246,2379,23628,239058,2450052,25351755,264270765,2771024652,

%T 29194911342,308813298690,3277454178144,34883317836240,

%U 372195546176496,3979793738688075,42635773396647054,457529396858568837,4917191231017846902,52917857164300253004

%N Coefficient of x^n in the expansion of 1/( (1-x)^3 * (1-x^2)^3 )^n.

%F a(n) = Sum_{k=0..floor(n/2)} binomial(3*n+k-1,k) * binomial(4*n-2*k-1,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 * (1-x^2)^3 ). See A368079.

%o (PARI) a(n, s=2, t=3, u=3) = sum(k=0, n\s, binomial(t*n+k-1, k)*binomial((u+1)*n-s*k-1, n-s*k));

%Y Cf. A368079.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Feb 13 2024