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%I #8 May 22 2019 20:59:39
%S 1,1,3,8,19,45,110,259,614,1466,3479,8239,19581,46445,110209,261555,
%T 620649,1472597,3494663,8292514,19677729,46694303,110804310,262932172,
%U 623928374,1480555791,3513297447,8336903884,19783134767,46944538382,111397439864,264341463510
%N G.f. A(x) satisfies: A(x) = x * Product_{k>=1} (1 + k*A(x^k)).
%F G.f. A(x) satisfies: A(x) = x * exp(-Sum_{k>=1} Sum_{d|k} d * (-d * A(x^d))^(k/d) / k).
%t terms = 32; A[_] = 0; Do[A[x_] = x Product[(1 + k A[x^k]), {k, 1, terms}] + O[x]^(terms + 1) // Normal, terms + 1]; CoefficientList[A[x], x] // Rest
%Y Cf. A050383, A091865, A308369, A308370, A308371.
%K nonn
%O 1,3
%A _Ilya Gutkovskiy_, May 22 2019
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