A371989 - OEIS

%I #9 Apr 15 2024 09:46:01

%S 1,6,18,-18,-270,486,7938,-17010,-290142,676998,11852082,-29091474,

%T -518183406,1315388646,23720180130,-61672468338,-1122411776958,

%U 2971089997830,54459919690578,-146181889695762,-2694816626063310,7314502270743270,135469313469987138

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

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

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

%Y Cf. A000302, A371990.

%Y Cf. A371681.

%K sign

%O 0,2

%A _Seiichi Manyama_, Apr 15 2024