A308031 -id:A308031 - cp's OEIS frontend

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

Ilya Gutkovskiy, May 10 2019

nonn

Shifts left 3 places under COMPOSE transform.

Cf. A030266, A030277, A308031, A308032.

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 *)

A308032 G.f. A(x) satisfies: A(x) = x + x^2 + x^3 + x^4 + x^5 * (1 + A(A(x))).

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 2, 4, 8, 16, 32, 66, 143, 333, 838, 2250, 6320, 18275, 53925, 161957, 495898, 1554159, 5008758, 16662249, 57311722, 203662894, 745602490, 2801326407, 10760995574, 42141768601, 167955587806, 680843078327, 2808084199432, 11793793850210, 50489830489534

Offset: 1

Ilya Gutkovskiy, May 10 2019

nonn

Shifts left 5 places under COMPOSE transform.

Cf. A030266, A030277, A308030, A308031.

terms = 35; A[] = 0; Do[A[x] = x + x^2 + x^3 + x^4 + x^5 (1 + A[A[x]]) + O[x]^(terms + 1) // Normal, terms + 1]; Rest[CoefficientList[A[x], x]]

cp's OEIS Frontend

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

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