A277829 First Series of Hankel determinants based on squares of Catalan numbers.

1, 1, 9, 1035, 1686931, 40768984675, 14961837668926225, 84566159505295329041875, 7428544024130633312561150929275, 10204389867956705680354458767618278532475, 220168039594282987862502167563496178988004727093379, 74853381374809235976722939648065921771360016655877341808897465

Offset: 0

Author

Karol A. Penson, Nov 27 2016

Keywords

• nonn

Comments

It would be very useful to have the formula for this sequence.

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..41

Crossrefs

Cf. A000108, A278770.

Programs

Maple

a:= n-> LinearAlgebra[Determinant](Matrix(n, (i, j)->
        (t-> (binomial(2*t, t)/(t+1))^2)(i+j-1))):
seq(a(n), n=0..15);  # Alois P. Heinz, Nov 28 2016

Mathematica

Flatten[{1, Table[Det[Table[(CatalanNumber[i + j - 1])^2, {i, n}, {j, n}]], {n,
  11}]}]

Formula

Conjecture: lim n->infinity log(a(n))/n^2 = 2*log(2). - Vaclav Kotesovec, Nov 29 2016

Extensions

a(0)=1 prepended by Alois P. Heinz, Nov 27 2016