A308030 G.f. A(x) satisfies: A(x) = x + x^2 + x^3 * (1 + A(A(x))).

1, 1, 1, 1, 2, 4, 8, 18, 45, 122, 350, 1052, 3313, 10933, 37739, 135865, 508545, 1973717, 7926795, 32895354, 140894024, 622160220, 2829323210, 13235526027, 63620528705, 313909404040, 1588405927920, 8235905545581, 43724990832997, 237527663672208, 1319398402129845

Offset

1,5

Comments

Shifts left 3 places under COMPOSE transform.

Links

Table of n, a(n) for n=1..31.

Mathematica

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]]
Nest[x + x^2 + x^3 + x^3 (# /. x -> #) &, O[x], 20][[3]] (* Vladimir Reshetnikov, Aug 08 2019 *)

Crossrefs

Cf. A030266, A030277, A308031, A308032.

Sequence in context: A245176 A000117 A338729 * A252653 A006771 A113989

Adjacent sequences: A308027 A308028 A308029 * A308031 A308032 A308033

Keyword

nonn

Author

Ilya Gutkovskiy, May 10 2019

Status

approved