0,3

G.f. A(x) satisfies: a(n+1) = [x^n] A(x)^(3^n) for n>=0, with a(0)=1.

G.f.: A(x) = 1 + x + 3*x^2 + 63*x^3 + 6732*x^4 + 3414312*x^5 +...

SERIES REPRESENTATION:

A(x) = 1 + x*[1 + log(A(3x)) + log(A(9x))^2/2! + log(A(27x))^3/3! +...+ log(A(3^n*x))^n/n! +...].

...

GENERATED BY POWERS OF G.F.:

a(n+1) equals the coefficient of x^n in A(x)^(3^n) for n>=0;

the coefficients of A(x)^(3^n) begin:

A^(3^0): [(1), 1, 3, 63, 6732, 3414312, 10221878106, ...];

A^(3^1): [1, (3), 12, 208, 20610, 10284678, 30686274630, ...];

A^(3^2): [1, 9, (63), 867, 66330, 31246902, 92246164932, ...];

A^(3^3): [1, 27, 432, (6732), 273024, 97968096, 278472473082, ...];

A^(3^4): [1, 81, 3483, 109863, (3414312), 385422948, 853280745822, ...];

A^(3^5): [1, 243, 30132, 2553768, 168586110, (10221878106), ...];

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)^(3^(#A-1)))[ #A])); A[n+1]}

Cf. A132695, A156905.

Sequence in context: A133275 A123687 A159605 this_sequence A053857 A037108 A092901

Adjacent sequences: A156901 A156902 A156903 this_sequence A156905 A156906 A156907

nonn

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