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%I #9 Sep 06 2022 15:09:18
%S 1,0,0,0,4,10,20,35,2856,30324,205920,1108965,23266540,482882686,
%T 6894708184,75981906455,1191424314640,28555511625320,635370500529216,
%U 11547272842560969,213976417787571540,5165550420447656050,142251473243071866520,3624660458114853235771
%N E.g.f. satisfies log(A(x)) = x^3/6 * (exp(x*A(x)) - 1) * A(x).
%F a(n) = n! * Sum_{k=0..floor(n/4)} (n-2*k+1)^(k-1) * Stirling2(n-3*k,k)/(6^k * (n-3*k)!).
%o (PARI) a(n) = n!*sum(k=0, n\4, (n-2*k+1)^(k-1)*stirling(n-3*k, k, 2)/(6^k*(n-3*k)!));
%Y Cf. A349557, A356785, A356962.
%Y Cf. A356952, A356968.
%K nonn
%O 0,5
%A _Seiichi Manyama_, Sep 06 2022
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