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%I #9 Aug 08 2019 21:07:27
%S 1,1,1,1,2,4,8,18,45,122,350,1052,3313,10933,37739,135865,508545,
%T 1973717,7926795,32895354,140894024,622160220,2829323210,13235526027,
%U 63620528705,313909404040,1588405927920,8235905545581,43724990832997,237527663672208,1319398402129845
%N G.f. A(x) satisfies: A(x) = x + x^2 + x^3 * (1 + A(A(x))).
%C Shifts left 3 places under COMPOSE transform.
%t terms = 31; A[_] = 0; Do[A[x_] = x + x^2 + x^3 (1 + A[A[x]]) + O[x]^(terms + 1) // Normal, terms + 1]; Rest[CoefficientList[A[x], x]]
%t Nest[x + x^2 + x^3 + x^3 (# /. x -> #) &, O[x], 20][[3]] (* _Vladimir Reshetnikov_, Aug 08 2019 *)
%Y Cf. A030266, A030277, A308031, A308032.
%K nonn
%O 1,5
%A _Ilya Gutkovskiy_, May 10 2019
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