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A036246 CONTINUANT transform of squares 1, 4, 9, ... 7

%I

%S 1,5,46,741,18571,669297,32814124,2100773233,170195445997,

%T 17021645372933,2059789285570890,296626678767581093,

%U 50131968501006775607,9826162452876095600065,2210936683865622516790232,566009617232052240393899457,163578990316746963096353733305

%N CONTINUANT transform of squares 1, 4, 9, ...

%C Denominator of fraction equal to the continued fraction [ 0, 1, 4, ...n^2 ].

%H Alois P. Heinz, <a href="/A036246/b036246.txt">Table of n, a(n) for n = 1..100</a>

%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>

%F a(n) ~ c * n^(2*n + 1) / exp(2*n), where c = 8.1245591771139376779472290412302409841950717664641832772206241208918274428499... - _Vaclav Kotesovec_, Jun 05 2018

%F From _Jianing Song_, Nov 30 2019: (Start)

%F a(n) = n^2 * a(n-1) + a(n-2) for n > 2.

%F Lim_{n->oo} A036245(n)/a(n) = A073824. (End)

%p a:= proc(n) option remember; `if`(n<0, 0,

%p `if`(n=0, 1, n^2 *a(n-1) +a(n-2)))

%p end:

%p seq(a(n), n=1..20); # _Alois P. Heinz_, Aug 06 2013

%t Table[Denominator[FromContinuedFraction[Range[0,n]^2]],{n,20}] (* _Harvey P. Dale_, Jul 16 2017 *)

%o (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 Cf. A036245, A073824.

%K frac,nonn

%O 1,2

%A _Jeff Burch_

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Last modified August 11 15:12 EDT 2020. Contains 336428 sequences. (Running on oeis4.)