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.

A036246 CONTINUANT transform of squares 1, 4, 9, ...

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%I A036246 #20 Nov 30 2019 09:10:36
%S A036246 1,5,46,741,18571,669297,32814124,2100773233,170195445997,
%T A036246 17021645372933,2059789285570890,296626678767581093,
%U A036246 50131968501006775607,9826162452876095600065,2210936683865622516790232,566009617232052240393899457,163578990316746963096353733305
%N A036246 CONTINUANT transform of squares 1, 4, 9, ...
%C A036246 Denominator of fraction equal to the continued fraction [ 0, 1, 4, ...n^2 ].
%H A036246 Alois P. Heinz, <a href="/A036246/b036246.txt">Table of n, a(n) for n = 1..100</a>
%H A036246 N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%F A036246 a(n) ~  c * n^(2*n + 1) / exp(2*n), where c = 8.1245591771139376779472290412302409841950717664641832772206241208918274428499... - _Vaclav Kotesovec_, Jun 05 2018
%F A036246 From _Jianing Song_, Nov 30 2019: (Start)
%F A036246 a(n) = n^2 * a(n-1) + a(n-2) for n > 2.
%F A036246 Lim_{n->oo} A036245(n)/a(n) = A073824. (End)
%p A036246 a:= proc(n) option remember; `if`(n<0, 0,
%p A036246       `if`(n=0, 1, n^2 *a(n-1) +a(n-2)))
%p A036246     end:
%p A036246 seq(a(n), n=1..20);  # _Alois P. Heinz_, Aug 06 2013
%t A036246 Table[Denominator[FromContinuedFraction[Range[0,n]^2]],{n,20}] (* _Harvey P. Dale_, Jul 16 2017 *)
%o A036246 (PARI) A036246(n) = my(v=vector(n+1)); for(i=1, n+1, if(i==1, v[i]=1, if(i==2, v[i]=1, v[i]=(i-1)^2*v[i-1]+v[i-2]))); v[n+1] \\ _Jianing Song_, Nov 30 2019
%Y A036246 Cf. A036245, A073824.
%K A036246 frac,nonn
%O A036246 1,2
%A A036246 _Jeff Burch_