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%I #16 Mar 02 2014 09:30:24
%S 1,-3,8,-23,74,-262,993,-3943,16178,-68000,291191,-1265618,5568263,
%T -24749363,110961248,-501209303,2278704938,-10419244888,47882934663,
%U -221047167628,1024586641973,-4766517165713,22248226873538,-104160733650738,489007907489239
%N a(n) = (-1)^n * Sum_{i=0..n} binomial(n+1,i+1)*Catalan(i).
%D J.-P. Allouche and J. Shallit, Automatic Sequences, Cambridge Univ. Press, 2003, p. 371.
%H Vincenzo Librandi, <a href="/A050511/b050511.txt">Table of n, a(n) for n = 0..1000</a>
%F G.f.: (sqrt((5*x+1)/(x+1))-1)/(2*x*(x+1)).
%F (n+1)*a(n)=(1-6*n)*a(n-1)-5*n*a(n-2)+(-1)^n. - _Vladeta Jovovic_, Jul 16 2004
%F a(n) ~ (-1)^n * 5^(n+5/2) / (32 * sqrt(Pi) * n^(3/2)). - _Vaclav Kotesovec_, Mar 02 2014
%t Table[(-1)^n Sum[Binomial[n+1,i+1]CatalanNumber[i],{i,0,n}],{n,0,30}] (* _Harvey P. Dale_, Jan 26 2013 *)
%Y Column 1 of A091698.
%K sign
%O 0,2
%A _N. J. A. Sloane_, Dec 28 1999