cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A277829 #39 May 01 2018 17:35:06
%S A277829 1,1,9,1035,1686931,40768984675,14961837668926225,
%T A277829 84566159505295329041875,7428544024130633312561150929275,
%U A277829 10204389867956705680354458767618278532475,220168039594282987862502167563496178988004727093379,74853381374809235976722939648065921771360016655877341808897465
%N A277829 First Series of Hankel determinants based on squares of Catalan numbers.
%C A277829 It would be very useful to have the formula for this sequence.
%H A277829 Alois P. Heinz, <a href="/A277829/b277829.txt">Table of n, a(n) for n = 0..41</a>
%F A277829 Conjecture: lim n->infinity log(a(n))/n^2 = 2*log(2). - _Vaclav Kotesovec_, Nov 29 2016
%p A277829 a:= n-> LinearAlgebra[Determinant](Matrix(n, (i, j)->
%p A277829         (t-> (binomial(2*t, t)/(t+1))^2)(i+j-1))):
%p A277829 seq(a(n), n=0..15);  # _Alois P. Heinz_, Nov 28 2016
%t A277829 Flatten[{1, Table[Det[Table[(CatalanNumber[i + j - 1])^2, {i, n}, {j, n}]], {n,
%t A277829   11}]}]
%Y A277829 Cf. A000108, A278770.
%K A277829 nonn
%O A277829 0,3
%A A277829 _Karol A. Penson_, Nov 27 2016
%E A277829 a(0)=1 prepended by _Alois P. Heinz_, Nov 27 2016