%I A144691
%S A144691 1,1,2,4,26,106,816,4292,90162,715138,10275886,87498566,1944309280,
%T A144691 20988667064,351769697800,3865796198136
%N A144691 a(n) = Limit_{m->infinity} [x^(2^m+n)] B(x)^(n+1)/(n+1) for n>=0, where 
               B(x) = Sum_{k>=0} x^(2^k); thus a(n) = A144690(n)/(n+1).
%C A144691 a(n) = limit, as m grows, of coefficient of x^(2^m+n) in B(x)^(n+1)/(n+1)
%C A144691 where B(x) = x + x^2 + x^4 + x^8 +...+ x^(2^k) +...
%F A144691 Given g.f. A(x), let G(x) = g.f. of A144692 where
%F A144691 A(x/G(x)) = G(x) = x/Series_Reversion[x/*A(x)] and G(x*A(x)) = A(x).
%e A144691 G.f.: A(x) = 1 + x + 2*x^2 + 4*x^3 + 26*x^4 + 106*x^5 + 816*x^6 +...
%e A144691 A(x/G(x)) = G(x) = x/Series_Reversion[x/*A(x)] where
%e A144691 G(x) = 1 + x + x^2 + 17*x^4 + 408*x^6 + 69473*x^8 + 6018928*x^10 +...
%e A144691 and G(x) appears to continue with only even powers of x (cf. A144692).
%o A144691 (PARI) {a(n)=local(m=n+3,B=sum(k=0,m,x^(2^k)));if(n<0,0,polcoeff((B+O(x^(2^m+n+1)))^(n+1)/
               (n+1),2^m+n))}
%Y A144691 Cf. A007178, A144690, A144692.
%Y A144691 Sequence in context: A129894 A028386 A155120 this_sequence A085700 A087404 
               A009237
%Y A144691 Adjacent sequences: A144688 A144689 A144690 this_sequence A144692 A144693 
               A144694
%K A144691 more,nonn
%O A144691 0,3
%A A144691 Paul D. Hanna (pauldhanna(AT)juno.com), Oct 10 2008