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A277829 First Series of Hankel determinants based on squares of Catalan numbers. 9
1, 1, 9, 1035, 1686931, 40768984675, 14961837668926225, 84566159505295329041875, 7428544024130633312561150929275, 10204389867956705680354458767618278532475, 220168039594282987862502167563496178988004727093379, 74853381374809235976722939648065921771360016655877341808897465 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

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

FORMULA

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

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}]}]

CROSSREFS

Cf. A000108, A278770.

Sequence in context: A004809 A099127 A172944 * A286396 A174636 A054344

Adjacent sequences:  A277826 A277827 A277828 * A277830 A277831 A277832

KEYWORD

nonn

AUTHOR

Karol A. Penson, Nov 27 2016

EXTENSIONS

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

STATUS

approved

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Last modified May 26 15:21 EDT 2019. Contains 323597 sequences. (Running on oeis4.)