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%I #11 May 04 2013 05:22:34
%S 1,3,11,41,152,561,2067,7618,28118,104006,385662,1433797,5344510,
%T 19973085,74827395,281000430,1057628550,3989213610,15077120010,
%U 57092280570,216579650664,822991216746,3132339521966,11939881979076,45577753704252,174218415470092,666795041653916
%N Expansion of (1+x*C^4)*C^2, where C = (1-(1-4*x)^(1/2))/(2*x) is g.f. for Catalan numbers, A000108.
%H Vincenzo Librandi, <a href="/A032952/b032952.txt">Table of n, a(n) for n = 0..200</a>
%F Recurrence: (n+5)*(19*n-8)*a(n) = (113*n^2+307*n-76)*a(n-1) - 2*(2*n-1)*(37*n+36)*a(n-2). - _Vaclav Kotesovec_, Oct 08 2012
%F a(n) ~ 13*2^(2*n+2)/(sqrt(Pi)*n^(3/2)). - _Vaclav Kotesovec_, Oct 08 2012
%t Table[SeriesCoefficient[(1+x*((1-(1-4*x)^(1/2))/(2*x))^4)*((1-(1-4*x)^(1/2))/(2*x))^2,{x,0,n}],{n,0,20}] (* _Vaclav Kotesovec_, Oct 08 2012 *)
%o (PARI) x='x+O('x^66); C=(1-(1-4*x)^(1/2))/(2*x); Vec( (1+x*C^4)*C^2 ) \\ _Joerg Arndt_, May 04 2013
%K nonn
%O 0,2
%A _N. J. A. Sloane_, Jun 06 2002
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