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%I #39 May 01 2018 17:35:06
%S 1,1,9,1035,1686931,40768984675,14961837668926225,
%T 84566159505295329041875,7428544024130633312561150929275,
%U 10204389867956705680354458767618278532475,220168039594282987862502167563496178988004727093379,74853381374809235976722939648065921771360016655877341808897465
%N First Series of Hankel determinants based on squares of Catalan numbers.
%C It would be very useful to have the formula for this sequence.
%H Alois P. Heinz, <a href="/A277829/b277829.txt">Table of n, a(n) for n = 0..41</a>
%F Conjecture: lim n->infinity log(a(n))/n^2 = 2*log(2). - _Vaclav Kotesovec_, Nov 29 2016
%p a:= n-> LinearAlgebra[Determinant](Matrix(n, (i, j)->
%p (t-> (binomial(2*t, t)/(t+1))^2)(i+j-1))):
%p seq(a(n), n=0..15); # _Alois P. Heinz_, Nov 28 2016
%t Flatten[{1, Table[Det[Table[(CatalanNumber[i + j - 1])^2, {i, n}, {j, n}]], {n,
%t 11}]}]
%Y Cf. A000108, A278770.
%K nonn
%O 0,3
%A _Karol A. Penson_, Nov 27 2016
%E a(0)=1 prepended by _Alois P. Heinz_, Nov 27 2016
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