A054114 - OEIS

%I #18 Apr 09 2020 09:35:16

%S 1,8,28,98,350,1274,4706,17576,66196,250952,956384,3660540,14061140,

%T 54177740,209295260,810375650,3143981870,12219117170,47564380970,

%U 185410909790,723668784230,2827767747950,11061198475550,43308802158650,169719408596402,665637941544506

%N T(2n+1,n), array T as in A054110.

%C Apart from the initial term, identical to A066796(n+1).

%F G.f.: (-1+3*x+5*x^2-4*x^3+sqrt(1-4*x))/(x*(1-x)*(1-4*x)). - _Ralf Stephan_, Apr 03 2004; corrected by _Georg Fischer_, Apr 09 2020

%F For n>0, a(n) = sum(k=1, n+1, C(2k, k)). - _Ralf Stephan_, Apr 03 2004

%t CoefficientList[Series[(-1+3*x+5*x^2-4*x^3+Sqrt[1-4*x])/(x*(1-x)(1-4*x)), {x,0,30}],x] (* _Georg Fischer_, Apr 09 2020 *)

%Y Cf. A054110, A066796.

%K nonn

%O 0,2

%A _Clark Kimberling_

%E Corrected by _Franklin T. Adams-Watters_, Oct 25 2006

%E a(23)-a(25) corrected by _Georg Fischer_, Apr 09 2020