A179471 - OEIS

%I #4 Oct 04 2013 20:44:24

%S 1,1,3,15,139,2387,79115,5148411,664332843,170744863371,

%T 87593505706987,89783692196468907,183966962290186844267,

%U 753712824966410639243755,6175169543791440589003293035,101180154484297968338398947674219

%N G.f. satisfies: A(x) = exp( Sum_{n>=1} A(2^n*x^n)*x^n/n ).

%C Compare to g.f. of A157675: G(x) = exp( Sum_{n>=1} G(2^n*x)^n*x^n/n ).

%F  Limit a(n) / 2^(n*(n-1)/2) = 2.494435637496531683539561928813688982084486211124...

%e G.f.: A(x) = 1 + x + 3*x^2 + 15*x^3 + 139*x^4 + 2387*x^5 +...

%e log(A(x)) = A(2x) + A(4x^2)*x^2/2 + A(8x^3)*x^3/3 + A(16x^4)*x^4/4 +...

%o (PARI) {a(n)=local(A=1+x);for(i=1,n,A=exp(sum(m=1,n,subst(A,x,2^m*x^m+x*O(x^n))*x^m/m)));polcoeff(A,n)}

%Y Cf. A157675.

%K nonn

%O 0,3

%A _Paul D. Hanna_, Jul 15 2010