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

%I #9 Mar 10 2024 07:50:35

%S 1,1,0,0,24,360,2160,7560,241920,8164800,145756800,1736380800,

%T 34488115200,1416906691200,46117316044800,1085696644032000,

%U 26627911620710400,1054301997805056000,46867776416068608000,1726488804870679449600,58404671366139850752000

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

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

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

%Y Cf. A365287, A370928.

%Y Cf. A161631, A371067.

%K nonn

%O 0,5

%A _Seiichi Manyama_, Mar 09 2024