A054114 T(2n+1,n), array T as in A054110.

1, 8, 28, 98, 350, 1274, 4706, 17576, 66196, 250952, 956384, 3660540, 14061140, 54177740, 209295260, 810375650, 3143981870, 12219117170, 47564380970, 185410909790, 723668784230, 2827767747950, 11061198475550, 43308802158650, 169719408596402, 665637941544506

Offset: 0

Author

Clark Kimberling

Keywords

• nonn

Comments

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

Crossrefs

Cf. A054110, A066796.

Programs

Mathematica

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 *)

Formula

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

For n>0, a(n) = sum(k=1, n+1, C(2k, k)). - Ralf Stephan, Apr 03 2004

Extensions

Corrected by Franklin T. Adams-Watters, Oct 25 2006

a(23)-a(25) corrected by Georg Fischer, Apr 09 2020