%I A103971
%S A103971 1,5,10,45,190,930,4660,24445,131190,719830,4013260,22684370,129661740,
%T A103971 748252580,4353379560,25508284445,150392391590,891549228430,
%U A103971 5310994644060,31775749689670,190860711108740,1150473009844380
%N A103971 Expansion of (1-sqrt(1-4x-16x^2))/(2x).
%C A103971 Image of c(x), the g.f. of the Catalan numbers A000108 under the mapping 
               g(x)->(1+4x)g(x(1+4x)). In general, the image of the Catalan numbers 
               under the mapping g(x)->(1+i*x)g(x(1+i*x)) is given by a(n)=sum{k=0..n, 
               i^(n-k)C(k)C(k+1,n-k)}.
%F A103971 G.f. : (1-sqrt(1-4x(1+4x))/(2x); a(n)=sum{k=0..n, 4^(n-k)C(k)C(k+1, n-k)}.
%Y A103971 Sequence in context: A136138 A122173 A083515 this_sequence A035406 A103932 
               A034190
%Y A103971 Adjacent sequences: A103968 A103969 A103970 this_sequence A103972 A103973 
               A103974
%K A103971 easy,nonn
%O A103971 0,2
%A A103971 Paul Barry (pbarry(AT)wit.ie), Feb 23 2005