A054113 T(2*n,n), array T as in A054110.

1, 5, 17, 57, 197, 701, 2549, 9413, 35153, 132393, 501905, 1912769, 7321081, 28122281, 108355481, 418590521, 1620751301, 6287963741, 24438234341, 95128761941, 370821819581, 1447337568461, 5655535495901, 22122396951101, 86617604317301, 339438817192805, 1331275883089013

Offset: 0

Author

Clark Kimberling

Keywords

• nonn

Links

• Stefano Spezia, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A054110, A079309.

Programs

Mathematica

CoefficientList[Series[( -1+4x+2*Sqrt[1-4x])/((1-x)(1-4x)),{x,0,26}],x] (* Stefano Spezia, May 11 2024 *)

Formula

G.f.: (-1+4*x+2*sqrt(1-4*x))/((1-x)*(1-4*x)). - Ralf Stephan, Apr 03 2004

a(n) = 4*s(n) + 1, with s(n) = A079309(n) = Sum_{k=1..n} C(2k+1, k+1). - Ralf Stephan, Apr 03 2004