A181444 G.f. satisfies: A(x) = 1 + x*Sum_{n>=0} log( A(2^n*x)^2 )^n/n!.

1, 1, 4, 60, 2480, 242296, 53763904, 28363717952, 41396018951936, 215328934357721024, 4740698193856769942528, 430771050114778618253200384, 151994706469390446336698323709952

Offset

0,3

Links

Table of n, a(n) for n=0..12.

Formula

a(n+1) = [x^n] A(x)^(2^(n+1)) for n>=0, with a(0)=1, where A(x) = Sum_{n>=0} a(n)*x^n.

Example

G.f.: A(x) = 1 + x + 4*x^2 + 60*x^3 + 2480*x^4 + 242296*x^5 +...
A(x) = 1 + x*[1 + log(A(2x)^2) + log(A(4x)^2)^2/2! + log(A(8x)^2)^3/3! + log(A(16x)^2)^4/4! + log(A(32x)^2)^5/5! +...].
Coefficients in the 2^n-th powers of A(x) begin:
A^(2^0)=[1, 1, 4, 60, 2480, 242296, 53763904, 28363717952,...];
A^(2^1)=[(1), 2, 9, 128, 5096, 490032, 108035840, 56837199680,...];
A^(2^2)=[1,(4), 22, 292, 10785, 1002752, 218139920, 114116667872,...];
A^(2^3)=[1, 8,(60), 760, 24390, 2104632, 444861660, 230028874632,...];
A^(2^4)=[1, 16, 184,(2480), 64540, 4690704, 926901832,...];
A^(2^5)=[1, 32, 624, 10848,(242296), 12359328, 2033807312,...];
A^(2^6)=[1, 64, 2272, 61632, 1568240,(53763904), 5278676128,...];
A^(2^7)=[1, 128, 8640, 414080, 16187360, 588318336,(28363717952),...];
A^(2^8)=[1, 256, 33664, 3040000, 213028800, 12475903232, 658516757120,(41396018951936),...]; ...
where the diagonal terms in parenthesis form this sequence (shift left).
The third column of this table is given by A257272 (observation by Bruno Berselli). - M. F. Hasler, Apr 27 2015

Prog

(PARI) {a(n)=local(A=1+sum(m=1, n-1, a(m)*x^m)); polcoeff(1+x*sum(m=0, n, log(subst(A^2, x, 2^m*x)+x*O(x^n))^m/m!), n)}

Crossrefs

Cf. A132695, A181445.

Sequence in context: A322450 A099705 A012488 * A177780 A012567 A132627

Adjacent sequences: A181441 A181442 A181443 * A181445 A181446 A181447

Keyword

nonn

Author

Paul D. Hanna, Oct 22 2010

Status

approved