%I #10 Nov 28 2024 09:04:39

%S 1,9,72,549,4077,29772,214884,1537677,10930923,77298849,544300992,

%T 3819184236,26718251868,186440019192,1298115301356,9020928853341,

%U 62582406445287,433509545320731,2998884192348888,20720206275346269,143005275737941437,986000187782876976

%N Expansion of (Sum_{k>=0} binomial(3*k,k) * x^k)^3.

%F a(n) = Sum_{i+j+k=n, i,j,k >= 0} binomial(3*i,i) * binomial(3*j,j) * binomial(3*k,k).

%F G.f.: B(x)^3 where B(x) is the g.f. of A005809.

%F 4*a(n) - 27*a(n-1) = 3*A005809(n) for n > 0.

%o (PARI) my(N=30, x='x+O('x^N)); Vec(sum(k=0, N, binomial(3*k, k)*x^k)^3)

%Y Cf. A000302, A378484.

%Y Cf. A005809.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Nov 28 2024