|
| |
|
|
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
|
| |
|
|
