0,3

G.f. A(x) satisfies: a(n+1) = [x^n] A(x)^(4^n) for n>=0, with a(0)=1.

G.f.: A(x) = 1 + x + 4*x^2 + 184*x^3 + 69568*x^4 + 238298048*x^5 +...

SERIES REPRESENTATION:

A(x) = 1 + x*[1 + log(A(4x)) + log(A(16x))^2/2! + log(A(64x))^3/3! +...+ log(A(4^n*x))^n/n! +...].

...

GENERATED BY POWERS OF G.F.:

a(n+1) equals the coefficient of x^n in A(x)^(4^n) for n>=0;

the coefficients of A(x)^(4^n) begin:

A^(4^0): [(1), 1, 4, 184, 69568, 238298048, 10444630574080, ...];

A^(4^1): [1, (4), 22, 788, 280625, 954038256, 41781386268864, ...];

A^(4^2): [1, 16, (184), 4464, 1167708, 3830011216, 167171472557448, ...];

A^(4^3): [1, 64, 2272, (69568), 6361840, 15577329728, 669428002912672, ...];

A^(4^4): [1, 256, 33664, 3071744, (238298048), 78858088704, ...];

A^(4^5): [1, 1024, 527872, 182811648, 47958593280, (10444630574080), ...];

In the above table, the diagonal forms this sequence shift left.

(PARI) {a(n)=local(A=[1, 1]); for(i=1, n, A=concat(A, Vec(Ser(A)^(4^(#A-1)))[ #A])); A[n+1]}

Cf. A132695, A156904.

Sequence in context: A082393 A024266 A146549 this_sequence A102194 A102191 A123116

Adjacent sequences: A156902 A156903 A156904 this_sequence A156906 A156907 A156908

nonn

Paul D. Hanna (pauldhanna(AT)juno.com), Mar 04 2009