%I A144690
%S A144690 1,2,6,16,130,636,5712,34336,811458,7151380,113034746,1049982792,
%T A144690 25276020640,293841338896,5276545467000,61852739170176
%N A144690 a(n) = Limit_{m->infinity} [x^(2^m+n)] B(x)^(n+1) for n>=0, where B(x) 
               = Sum_{k>=0} x^(2^k).
%C A144690 The g.f. of A144691(n) = a(n)/(n+1) appears to have an interesting functional 
               interpretation.
%F A144690 a(n) = (n+1)*A144691(n).
%e A144690 a(n) = limit, as m grows, of coefficient of x^(2^m+n) in B(x)^(n+1)
%e A144690 where B(x) = x + x^2 + x^4 + x^8 +...+ x^(2^k) +...
%o A144690 (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),
               2^m+n))}
%Y A144690 Cf. A007178, A144691, A144692.
%Y A144690 Sequence in context: A147941 A147932 A147923 this_sequence A118305 A139629 
               A057497
%Y A144690 Adjacent sequences: A144687 A144688 A144689 this_sequence A144691 A144692 
               A144693
%K A144690 more,nonn
%O A144690 0,2
%A A144690 Paul D. Hanna (pauldhanna(AT)juno.com), Oct 10 2008