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%I #5 Apr 07 2019 09:07:55
%S 1,1,2,9,28,109,440,1790,7537,32300,140438,618608,2753510,12366672,
%T 55973926,255059808,1169143476,5387268256,24940059514,115943355422,
%U 541047868905,2533458659581,11900017205866,56055896316345,264748474342341,1253414056154014,5947373587731308
%N G.f. A(x) satisfies: A(x) = 1 + Sum_{k>=1} k*x^k*A(x)^k/(1 + x^k).
%F G.f. A(x) satisfies: A(x) = 1 + Sum_{k>=1} x^k * Sum_{d|k} (-1)^(k/d+1)*d*A(x)^d.
%e G.f.: A(x) = 1 + x + 2*x^2 + 9*x^3 + 28*x^4 + 109*x^5 + 440*x^6 + 1790*x^7 + 7537*x^8 + 32300*x^9 + 140438*x^10 + ...
%t terms = 27; A[_] = 0; Do[A[x_] = 1 + Sum[k x^k A[x]^k/(1 + x^k), {k, 1, j}] + O[x]^j, {j, 1, terms}]; CoefficientList[A[x], x]
%t terms = 27; A[_] = 0; Do[A[x_] = 1 + Sum[x^k Sum[(-1)^(k/d + 1) d A[x]^d, {d, Divisors[k]}], {k, 1, j}] + O[x]^j, {j, 1, terms}]; CoefficientList[A[x], x]
%Y Cf. A000593, A192207, A192401, A307396, A307398.
%K nonn
%O 0,3
%A _Ilya Gutkovskiy_, Apr 07 2019
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