login
G.f. A(x) satisfies A(x) = ( 1 + 9*x*(1 + x)*A(x) )^(1/3).
2

%I #7 Apr 17 2024 08:33:56

%S 1,3,3,-9,0,81,-171,-621,3672,324,-54918,125145,563922,-3381345,

%T -1013553,59036607,-128956455,-693917604,3979050642,2186515944,

%U -76048363647,153593093106,978492895848,-5278059507771,-4343581909296,107892778958370,-197193416230692

%N G.f. A(x) satisfies A(x) = ( 1 + 9*x*(1 + x)*A(x) )^(1/3).

%F a(n) = Sum_{k=0..n} 9^k * binomial(k/3+1/3,k) * binomial(k,n-k)/(k+1).

%o (PARI) a(n) = sum(k=0, n, 9^k*binomial(k/3+1/3, k)*binomial(k, n-k)/(k+1));

%Y Cf. A372036.

%K sign

%O 0,2

%A _Seiichi Manyama_, Apr 16 2024