%I #8 Apr 17 2024 08:33:49

%S 1,3,3,-6,3,57,-141,-321,2460,-1572,-29400,92505,196905,-1841208,

%T 1608636,24028995,-85167204,-161127519,1756947801,-1901675715,

%U -23476298442,91225005105,149447955855,-1890518796654,2421742054233,25239556328043,-106352841162777

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

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

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

%Y Cf. A372017.

%K sign

%O 0,2

%A _Seiichi Manyama_, Apr 16 2024