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%I #6 May 13 2022 10:00:15
%S 1,0,1,0,2,-3,4,-4,4,-10,14,-25,30,-48,48,-86,128,-192,286,-470,578,
%T -1000,1386,-2423,3172,-5198,7102,-11994,16414,-25820,38056,-61444,
%U 86658,-141564,203396,-324640,475536,-767110,1100728,-1810752,2601166,-4118166,6114666
%N Product_{n>=1} 1 / (1 - a(n)*x^n) = 1 + Sum_{n>=1} phi(n)*x^n, where phi = A000010.
%t A[m_, n_] := A[m, n] = Which[m == 1, EulerPhi[n], m > n >= 1, 0, True, A[m - 1, n] - A[m - 1, m - 1] A[m - 1, n - m + 1]]; a[n_] := A[n, n]; a /@ Range[1, 43]
%Y Cf. A000010, A320778, A328774, A353925, A353945, A353947, A353949.
%K sign
%O 1,5
%A _Ilya Gutkovskiy_, May 12 2022
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