A156905 G.f. A(x) satisfies: A(x) = 1 + x*Sum_{n>=0} log( A(4^n*x) )^n / n!.

1, 1, 4, 184, 69568, 238298048, 10444630574080, 6785507740131518464, 63569094414156159478579200, 8469123482983731772132032235429888, 16127763920864889230376762555181238559440896

Offset: 0

Author

Paul D. Hanna, Mar 04 2009

Keywords

• nonn

Examples

			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.
		

Crossrefs

Cf. A132695, A156904.

Programs

PARI

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

Formula

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