A307660 E.g.f. A(x) satisfies: A(x) = exp(-x) * A(x^2)*A(x^3)*A(x^4)* ... *A(x^k)* ...

1, -1, -1, -1, -23, 139, -929, 12011, -54319, 664343, 7497631, 17751799, -1294263431, 13183537379, 335384855807, -8293330879261, 26192873684641, -1587651616174289, 12035003736999871, -887536237005983377, 13114291271436277001, -332542758207041951941, 2683832751567973018399

Offset: 0

Author

Ilya Gutkovskiy, Apr 20 2019

Keywords

• sign

Examples

			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! + ...
		

Crossrefs

Cf. A074206, A129375, A307661.

Programs

Mathematica

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]!

Formula

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

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