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%I #9 May 22 2019 20:59:21
%S 1,1,4,12,41,133,485,1752,6677,25809,102130,409532,1665128,6837348,
%T 28333334,118288386,497120101,2101181482,8926401690,38093403136,
%U 163224292328,701951448268,3028792691947,13108224143298,56887750453404,247512117880754,1079421026637431
%N G.f. A(x) satisfies: A(x) = x * Product_{k>=1} 1/(1 - A(x^k))^k.
%F G.f. A(x) satisfies: A(x) = x * exp(Sum_{k>=1} Sum_{d|k} d^2 * A(x^d)^(k/d) / k).
%t terms = 27; A[_] = 0; Do[A[x_] = x Product[1/(1 - A[x^k])^k, {k, 1, terms}] + O[x]^(terms + 1) // Normal, terms + 1]; CoefficientList[A[x], x] // Rest
%Y Cf. A050383, A091865, A308370, A308371, A308372.
%K nonn
%O 1,3
%A _Ilya Gutkovskiy_, May 22 2019