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A303826 Hankel transform of A001246. 0
1, 3, 99, 43881, 280974025, 26916213134875, 39339805703866118875, 887919033897631593738548625, 311967217568836709207331125906048625, 1715750319988362944273302140220635494624999475 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

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

LINKS

Table of n, a(n) for n=0..9.

Wikipedia, Hankel matrix

EXAMPLE

a(2) = 99 because determinant of the following matrix is 99.

[1  1   4]

[1  4  25]

[4 25 196]

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}]

PROG

(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

CROSSREFS

Cf. A000108, A001246, A277829, A278770.

Sequence in context: A276188 A180350 A293952 * A128296 A037114 A336437

Adjacent sequences:  A303823 A303824 A303825 * A303827 A303828 A303829

KEYWORD

nonn

AUTHOR

Karol A. Penson, May 01 2018

EXTENSIONS

Name simplified by Andrey Zabolotskiy, May 02 2018

STATUS

approved

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Last modified August 17 15:35 EDT 2022. Contains 356189 sequences. (Running on oeis4.)