A146533 Catalan transform of A135092.

1, 7, 21, 70, 245, 882, 3234, 12012, 45045, 170170, 646646, 2469012, 9464546, 36402100, 140408100, 542911320, 2103781365, 8167621770, 31762973550, 123708423300, 482462850870, 1883902560540, 7364346373020, 28817007546600, 112866612890850, 442437122532132, 1735714865318364

Offset: 0

Author

Philippe Deléham, Oct 31 2008

Keywords

• nonn

Crossrefs

Cf. A088218, A000984, A029651, A100320, A029609, A144706.

Programs

Mathematica

a[n_]:=(7*Binomial[2n,n]-5*KroneckerDelta[n,0])/2; Array[a,27,0] (* Stefano Spezia, Feb 14 2025 *)

Formula

a(n) = Sum_{k=0..n} A039599(n,k)*A010687(k) = Sum_{k=0..n} A106566(n,k)*A135092(k).

a(n) = (7*C(2n,n) - 5*0^n)/2.

From Stefano Spezia, Feb 14 2025: (Start)

G.f.: (7/sqrt(1 - 4*x) - 5)/2.

E.g.f.: (7*exp(2*x)*BesselI(0, 2*x) - 5)/2. (End)

Extensions

a(23)-a(26) from Stefano Spezia, Feb 14 2025