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%I #6 Apr 07 2019 09:07:43
%S 1,1,4,13,52,209,906,4010,18303,85064,402008,1924412,9314594,45502924,
%T 224068334,1111017056,5542331502,27796367468,140072333426,
%U 708875098462,3601278993411,18359296689521,93892611212526,481575492271765,2476572824391335,12767331527712854
%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} d*A(x)^d.
%e G.f.: A(x) = 1 + x + 4*x^2 + 13*x^3 + 52*x^4 + 209*x^5 + 906*x^6 + 4010*x^7 + 18303*x^8 + 85064*x^9 + 402008*x^10 + ...
%t terms = 26; 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 = 26; A[_] = 0; Do[A[x_] = 1 + Sum[x^k Sum[d A[x]^d, {d, Divisors[k]}], {k, 1, j}] + O[x]^j, {j, 1, terms}]; CoefficientList[A[x], x]
%Y Cf. A000203, A192207, A307396, A307400.
%K nonn
%O 0,3
%A _Ilya Gutkovskiy_, Apr 07 2019
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