A278770 Second series of Hankel determinants based on squares of Catalan numbers.

1, 4, 159, 81296, 585396881, 61994262028020, 98925461617709743975, 2414583243140269424293854400, 910504281815476426073145299359052745, 5341354769384557074743892800174971438265757284, 489946515248844365403775650233194419858267427195735348151, 705379807799940807283682167156246485805791300481296966713394135535056

Offset: 0

Author

Karol A. Penson, Nov 28 2016

Keywords

• nonn

Comments

It would be useful to know the formula for this sequence.

Crossrefs

Cf. A000108, A277829.

Programs

Maple

a:= n-> LinearAlgebra[Determinant](Matrix(n, (i, j)->
        (t-> (binomial(2*t, t)/(t+1))^2)(i+j))):
seq(a(n), n=0..12);  # Alois P. Heinz, May 01 2018

Mathematica

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

Formula

Conjecture: lim n->infinity log(a(n))/n^2 = 2*log(2). - Vaclav Kotesovec, Nov 28 2016