A380039 - OEIS

%I #9 Jan 11 2025 10:27:57

%S 1,1,6,61,908,17865,438286,12901735,443475432,17443879057,

%T 773018191610,38117147134671,2070381313048588,122841147634754185,

%U 7905667340470592070,548555101319868261655,40825552788531622527056,3244188226183716688784289,274164589130871765969460594

%N E.g.f. A(x) satisfies A(x) = 1/( 1 - 3*x*exp(x*A(x)) )^(1/3).

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

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

%Y Cf. A380017, A380041.

%Y Cf. A380040.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Jan 10 2025