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

%I #9 Mar 17 2024 04:08:31

%S 1,0,2,3,148,905,40506,542437,25080392,562677201,28058678110,

%T 908452740701,49777760550684,2120072013408505,128583516119137730,

%U 6778703037793746165,455574282215526201616,28520235381763443992993,2118889776612629769160518

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

%F a(n) = n! * (3*n)! * Sum_{k=0..floor(n/2)} Stirling2(n-k,k)/( (n-k)! * (3*n-k+1)! ).

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

%Y Cf. A371231.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Mar 16 2024