A120259 Row sums of number triangle A120258.

1, 2, 4, 11, 46, 302, 3109, 49345, 1209058, 45574112, 2636237374, 234854695297, 32081882854399, 6733481882732516, 2172532761103119601, 1074257501384373622001, 816914977299535380309346, 953227711986515337529688144, 1706089496424625166250326935690

Offset: 0

Author

Paul Barry, Jun 13 2006

Keywords

• easy
• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..103

Crossrefs

Cf. A120258.

Programs

Mathematica

Table[Sum[Product[Binomial[2*n-2*k+j, n-k]/Binomial[n-k+j, j],{j,0,k-1}],{k,0,n}],{n,0,20}] (* Vaclav Kotesovec, Apr 02 2021 *)
Table[Sum[BarnesG[k+1] * BarnesG[n-k+1]^2 * BarnesG[2*n-k+1] / BarnesG[2*n-2*k+1], {k, 0, n}] / BarnesG[n+1]^2, {n, 0, 20}] (* Vaclav Kotesovec, Apr 02 2021 *)

Formula

a(n) = sum{k=0..n, Product{j=0..k-1, C(2n-2k+j, n-k)/C(n-k+j, j)}}

Limit_{n->infinity} a(n)^(1/n^2) = r^(r/2) * (2-r)^(1 - r/2) = 1.238819877352130037160235229707224180528582190767293210626357503368..., where r = 0.370130616271672149875211085663371877443670059442239590157339853950... is the root of the equation (4 - 4*r)^(2 - 2*r) * r^r = (2-r)^(2-r). - Vaclav Kotesovec, Apr 02 2021