A380040 - OEIS

%I #9 Jan 11 2025 10:27:46

%S 1,2,14,170,3000,69930,2033212,70972734,2894590064,135164076722,

%T 7113787010100,416759006663142,26903080612468744,1897553477118350922,

%U 145204649027247413996,11982094054396851014030,1060673494236770414806752,100265097180082772515691874,10080871201186661027182272868

%N E.g.f. A(x) satisfies A(x) = 1/( 1 - 3*x*exp(x*A(x)) )^(2/3).

%F E.g.f.: B(x)^2, where B(x) is the e.g.f. of A380041.

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

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

%Y Cf. A380039, A380041.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Jan 10 2025