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%I #12 Aug 15 2023 12:01:33
%S 1,1,10,183,5140,196005,9468486,554425963,38171336680,3022130473065,
%T 270537702834250,27021535857472431,2979254055371578524,
%U 359411244032212931533,47093111659782104431438,6660135357832421444841555,1011181346455643980818939856
%N E.g.f. satisfies A(x) = 1 + x*exp(x)*A(x)^4.
%F a(n) = n! * Sum_{k=0..n} k^(n-k) * binomial(4*k+1,k)/( (4*k+1)*(n-k)! ) = n! * Sum_{k=0..n} k^(n-k) * A002293(k)/(n-k)!.
%o (PARI) a(n) = n!*sum(k=0, n, k^(n-k)*binomial(4*k, k)/((3*k+1)*(n-k)!));
%Y Cf. A006153, A295238, A364983.
%Y Cf. A002293, A349331.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Aug 15 2023
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