A303826 Hankel transform of A001246.

1, 3, 99, 43881, 280974025, 26916213134875, 39339805703866118875, 887919033897631593738548625, 311967217568836709207331125906048625, 1715750319988362944273302140220635494624999475

Offset: 0

Author

Karol A. Penson, May 01 2018

Keywords

• nonn

Comments

a(n) is the determinant of the (n+1) X (n+1) matrix A defined by A[i,j] = A001246(i+j-2) for 1 <= i,j <= n+1. - Altug Alkan, May 01 2018

Examples

			a(2) = 99 because determinant of the following matrix is 99.
[1  1   4]
[1  4  25]
[4 25 196]
		

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..41
• Wikipedia, Hankel matrix

Crossrefs

Cf. A000108, A001246, A277829, A278770.

Programs

Maple

a:= n-> LinearAlgebra[Determinant](Matrix(n+1, (i, j)->
        (t-> (binomial(2*t, t)/(t+1))^2)(i+j-2))):
seq(a(n), n=0..15);  # Alois P. Heinz, May 01 2018

Mathematica

Table[Det[
  Table[(CatalanNumber[i + j - 2])^2, {i, 1, n + 1}, {j, 1, n + 1}]], {n,
  0, 10}]

PARI

a(n) = matdet(matrix(n+1, n+1, i, j, (binomial(2*(i+j-2),(i+j-2))/(i+j-1))^2)); \\ Altug Alkan, May 01 2018

Formula

a(n)^(1/n) ~ d * 4^n, where d = 0.263565... - Vaclav Kotesovec, May 06 2024

Extensions

Name simplified by Andrey Zabolotskiy, May 02 2018