%I #9 Nov 07 2023 08:23:44
%S 1,1,9,160,4367,161796,7592593,431826760,28875060411,2220199609420,
%T 193010401410437,18720726373805952,2004328775014537111,
%U 234797380878372574276,29873926565253226992921,4102473564838214815027576,604804589755948599369229811
%N E.g.f. satisfies A(x) = 1 + A(x)^3 * (exp(x*A(x)) - 1).
%F a(n) = Sum_{k=0..n} (n+3*k)!/(n+2*k+1)! * Stirling2(n,k).
%o (PARI) a(n) = sum(k=0, n, (n+3*k)!/(n+2*k+1)!*stirling(n, k, 2));
%Y Cf. A000272, A052894, A367162.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Nov 07 2023
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