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E.g.f. A(x) satisfies: A(x) = exp(-x) * A(x^2)*A(x^3)*A(x^4)* ... *A(x^k)* ...
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%I #7 Apr 21 2019 07:50:51

%S 1,-1,-1,-1,-23,139,-929,12011,-54319,664343,7497631,17751799,

%T -1294263431,13183537379,335384855807,-8293330879261,26192873684641,

%U -1587651616174289,12035003736999871,-887536237005983377,13114291271436277001,-332542758207041951941,2683832751567973018399

%N E.g.f. A(x) satisfies: A(x) = exp(-x) * A(x^2)*A(x^3)*A(x^4)* ... *A(x^k)* ...

%F E.g.f.: exp(-Sum_{n>=1} A074206(k)*x^k).

%F a(0) = 1; a(n) = -Sum_{k=1..n} A074206(k)*k!*binomial(n-1,k-1)*a(n-k).

%e E.g.f.: A(x) = 1 - x - x^2/2! - x^3/3! - 23*x^4/4! + 139*x^5/5! - 929*x^6/6! + 12011*x^7/7! - 54319*x^8/! + 664343*x^9/9! + ...

%t terms = 22; A[_] = 1; Do[A[x_] = Exp[-x] Product[A[x^k], {k, 2, terms}] + O[x]^(terms + 1) // Normal, terms + 1]; CoefficientList[A[x], x] Range[0, terms]!

%Y Cf. A074206, A129375, A307661.

%K sign

%O 0,5

%A _Ilya Gutkovskiy_, Apr 20 2019