A371743 - OEIS

%I #10 Apr 05 2024 13:06:33

%S 1,4,29,231,1926,16491,143683,1267395,11282393,101151544,912011633,

%T 8260998772,75115815749,685232639419,6268299350776,57478389714473,

%U 528167137069958,4862304525663579,44836026545219765,414048025058547788,3828677665694353049

%N a(n) = Sum_{k=0..floor(n/2)} binomial(4*n-k,n-2*k).

%F a(n) = [x^n] 1/((1-x-x^2) * (1-x)^(3*n)).

%F a(n) ~ 2^(8*n + 5/2) / (11 * sqrt(Pi*n) * 3^(3*n - 1/2)). - _Vaclav Kotesovec_, Apr 05 2024

%o (PARI) a(n) = sum(k=0, n\2, binomial(4*n-k, n-2*k));

%Y Cf. A108081, A371742, A371744.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Apr 05 2024