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A303826 Hankel transform of A001246.

%I A303826 #42 May 06 2024 05:18:21
%S A303826 1,3,99,43881,280974025,26916213134875,39339805703866118875,
%T A303826 887919033897631593738548625,311967217568836709207331125906048625,
%U A303826 1715750319988362944273302140220635494624999475
%N A303826 Hankel transform of A001246.
%C A303826 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
%H A303826 Vaclav Kotesovec, <a href="/A303826/b303826.txt">Table of n, a(n) for n = 0..41</a>
%H A303826 Wikipedia, <a href="https://en.wikipedia.org/wiki/Hankel_matrix">Hankel matrix</a>
%F A303826 a(n)^(1/n) ~ d * 4^n, where d = 0.263565... - _Vaclav Kotesovec_, May 06 2024
%e A303826 a(2) = 99 because determinant of the following matrix is 99.
%e A303826 [1  1   4]
%e A303826 [1  4  25]
%e A303826 [4 25 196]
%p A303826 a:= n-> LinearAlgebra[Determinant](Matrix(n+1, (i, j)->
%p A303826         (t-> (binomial(2*t, t)/(t+1))^2)(i+j-2))):
%p A303826 seq(a(n), n=0..15);  # _Alois P. Heinz_, May 01 2018
%t A303826 Table[Det[
%t A303826   Table[(CatalanNumber[i + j - 2])^2, {i, 1, n + 1}, {j, 1, n + 1}]], {n,
%t A303826   0, 10}]
%o A303826 (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
%Y A303826 Cf. A000108, A001246, A277829, A278770.
%K A303826 nonn
%O A303826 0,2
%A A303826 _Karol A. Penson_, May 01 2018
%E A303826 Name simplified by _Andrey Zabolotskiy_, May 02 2018