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

0,2

Links

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

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

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 *)

Crossrefs

Cf. A120258.

Sequence in context: A140838 A114954 A134019 * A174632 A307592 A091240

Adjacent sequences: A120256 A120257 A120258 * A120260 A120261 A120262

Keyword

easy,nonn

Author

Paul Barry, Jun 13 2006

Status

approved