%I #9 Jun 30 2018 19:09:57
%S 1,2,2,24,1096,149632,62966568,85329761952,386069877057040,
%T 6001439689098721408,327962184329946415530336,
%U 64150844215771337825753078272,45547009330254120256598494596400320,118653960132660605481807477808249363616768,1143717244821821894255831791273094878164139953920,41063965948289078797110473909472925848872401288025550336
%N O.g.f. A(x) satisfies: Sum_{n>=0} log( (1 + 2^n*x) / A(x) )^n / n! = 1.
%e O.g.f. A(x) = 1 + 2*x + 2*x^2 + 24*x^3 + 1096*x^4 + 149632*x^5 + 62966568*x^6 + 85329761952*x^7 + 386069877057040*x^8 + 6001439689098721408*x^9 + ...
%e such that Sum_{n>=0} log( (1 + 2^n*x) / A(x) )^n / n! = 1.
%e RELATED SERIES.
%e log(A(x)) = 2*x + 68*x^3/3 + 4200*x^4/4 + 737432*x^5/5 + 376015248*x^6/6 + 596428719840*x^7/7 + 3087194714985696*x^8/8 + ... + A306061(n)*x^n/n + ...
%o (PARI) {a(n) = my(A=[1]); for(i=1,n, A=concat(A,0); A[#A] = Vec( sum(m=0,#A, log( (1+2^m*x +x*O(x^#A)) / Ser(A) )^m/m! ) )[#A] ); A[n+1]}
%o for(n=0,20,print1(a(n),", "))
%Y Cf. A306061, A316369.
%K nonn
%O 0,2
%A _Paul D. Hanna_, Jun 19 2018