A372124 - OEIS

%I #11 Apr 20 2024 10:27:46

%S 1,1,5,8,86,12,2418,-6015,97271,-490693,4991069,-33481184,294850612,

%T -2232642956,18815166552,-150373925928,1255171140378,-10300278908424,

%U 86135158514634,-717384480699522,6029697856319760,-50699911500290454,428507430151063548

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

%F G.f.: A(x) = 2/(1 + sqrt(1-4*x*(1+9*x)^(1/3))).

%F a(n) = Sum_{k=0..n} 9^(n-k) * binomial(2*k,k) * binomial(k/3,n-k)/(k+1).

%o (PARI) my(N=30, x='x+O('x^N)); Vec(2/(1+sqrt(1-4*x*(1+9*x)^(1/3))))

%o (PARI) a(n) = sum(k=0, n, 9^(n-k)*binomial(2*k, k)*binomial(k/3, n-k)/(k+1));

%Y Cf. A000108, A372137.

%K sign

%O 0,3

%A _Seiichi Manyama_, Apr 20 2024