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%I #4 Jul 04 2020 01:44:42
%S 1,-1,-2,-2,2,12,0,-190,-696,1960,29592,49750,-1200226,-8200478,
%T 51479530,992408898,-517104450,-133585331394,-757952722052,
%U 18448429372430,284177581205280,-2033645276651570,-87779867499696610,-122540992214640738,26825921931152034414
%N E.g.f. A(x) satisfies: A'(x) = 1 + A(1 - exp(x)).
%F a(1) = 1; a(n) = Sum_{k=1..n-1} (-1)^k * Stirling2(n-1,k) * a(k).
%t terms = 25; A[_] = 0; Do[A[x_] = Normal[Integrate[1 + A[1 - Exp[x] + O[x]^(terms + 1)], x] + O[x]^(terms + 1)], terms]; CoefficientList[A[x], x] Range[0, terms]! // Rest
%t a[1] = 1; a[n_] := a[n] = Sum[(-1)^k StirlingS2[n - 1, k] a[k], {k, 1, n - 1}]; Table[a[n], {n, 1, 25}]
%Y Cf. A003659.
%K sign
%O 1,3
%A _Ilya Gutkovskiy_, Jul 03 2020
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