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A303826 Hankel transform of A001246. 1
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
Wikipedia, Hankel matrix
FORMULA
a(n)^(1/n) ~ d * 4^n, where d = 0.263565... - Vaclav Kotesovec, May 06 2024
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
Sequence in context: A276188 A180350 A293952 * A128296 A037114 A336437
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 June 15 10:19 EDT 2024. Contains 373407 sequences. (Running on oeis4.)