A087959 G.f. satisfies A(x) = 1 + x*A(x*A(x*A(x))).

1, 1, 1, 2, 6, 22, 95, 463, 2483, 14426, 89799, 594038, 4150514, 30482791, 234428282, 1881944298, 15729230166, 136566166388, 1229346044429, 11454129882773, 110293243452027, 1096078120808889, 11227947692444477, 118421577443291274, 1284625091089249880

Offset: 0

Author

Paul D. Hanna, Sep 16 2003

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..100

Crossrefs

Cf. A087949.

Programs

Maple

A:= proc(n) option remember; local T; if n=0 then 1 else T:= A(n-1); unapply(convert(series(1+ x*T(x*T(x*T(x))), x, n+1), polynom), x) fi end: a:= n-> coeff(A(n)(x), x, n): seq(a(n), n=0..21);  # Alois P. Heinz, Aug 23 2008

Mathematica

A[n_] := A[n] = Module[{T}, If[n == 0, 1, T[y_] = A[n-1][y]; Normal[Series[1+x*T[x*T[x*T[x]]], {x, 0, n+1}]] /. x -> #]&]; a[n_] := Coefficient[A[n][x], x, n]; Table [a[n], {n, 0, 24}] (* Jean-François Alcover, Feb 14 2014, after Alois P. Heinz *)