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A307397 G.f. A(x) satisfies: A(x) = 1 + Sum_{k>=1} x^k*A(x)^k/(1 + x^k*A(x)^k). 2

%I

%S 1,1,1,3,8,18,50,150,429,1258,3835,11740,36148,112856,355318,1124582,

%T 3582186,11477162,36939043,119387415,387393424,1261422550,4120343870,

%U 13498085604,44337516318,145993301239,481812344551,1593439356575,5280074015618,17528034861180

%N G.f. A(x) satisfies: A(x) = 1 + Sum_{k>=1} x^k*A(x)^k/(1 + x^k*A(x)^k).

%F G.f. A(x) satisfies: A(x) = 1 + Sum_{k>=1} A048272(k)*x^k*A(x)^k.

%F G.f.: A(x) = (1/x)*Series_Reversion(x/(1 + Sum_{k>=1} A048272(k)*x^k)).

%e G.f.: A(x) = 1 + x + x^2 + 3*x^3 + 8*x^4 + 18 x^5 + 50*x^6 + 150*x^7 + 429*x^8 + 1258*x^9 + 3835*x^10 + ...

%t terms = 30; A[_] = 0; Do[A[x_] = 1 + Sum[x^k A[x]^k/ (1 + x^k A[x]^k), {k, 1, j}] + O[x]^j, {j, 1, terms}]; CoefficientList[A[x], x]

%t terms = 30; A[_] = 0; Do[A[x_] = 1 + Sum[Sum[(-1)^(d + 1), {d, Divisors[k]}] x^k A[x]^k, {k, 1, j}] + O[x]^j, {j, 1, terms}]; CoefficientList[A[x], x]

%t terms = 30; CoefficientList[1/x InverseSeries[Series[x/(1 + Sum[Sum[(-1)^(d + 1), {d, Divisors[k]}] x^k, {k, 1, terms}]), {x, 0, terms}], x], x]

%Y Cf. A048272, A190790, A192206, A307399, A307401.

%K nonn

%O 0,4

%A _Ilya Gutkovskiy_, Apr 07 2019

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Last modified April 17 18:52 EDT 2021. Contains 343070 sequences. (Running on oeis4.)