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A277829
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First Series of Hankel determinants based on squares of Catalan numbers.
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9
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1, 1, 9, 1035, 1686931, 40768984675, 14961837668926225, 84566159505295329041875, 7428544024130633312561150929275, 10204389867956705680354458767618278532475, 220168039594282987862502167563496178988004727093379, 74853381374809235976722939648065921771360016655877341808897465
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OFFSET
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0,3
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COMMENTS
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It would be very useful to have the formula for this sequence.
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LINKS
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FORMULA
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Conjecture: lim n->infinity log(a(n))/n^2 = 2*log(2). - Vaclav Kotesovec, Nov 29 2016
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MAPLE
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a:= n-> LinearAlgebra[Determinant](Matrix(n, (i, j)->
(t-> (binomial(2*t, t)/(t+1))^2)(i+j-1))):
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MATHEMATICA
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Flatten[{1, Table[Det[Table[(CatalanNumber[i + j - 1])^2, {i, n}, {j, n}]], {n,
11}]}]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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