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

1, 5, 46, 741, 18571, 669297, 32814124, 2100773233, 170195445997, 17021645372933, 2059789285570890, 296626678767581093, 50131968501006775607, 9826162452876095600065, 2210936683865622516790232, 566009617232052240393899457, 163578990316746963096353733305

Offset

1,2

Comments

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

Links

Alois P. Heinz, Table of n, a(n) for n = 1..100

N. J. A. Sloane, Transforms

Formula

a(n) ~ c * n^(2*n + 1) / exp(2*n), where c = 8.1245591771139376779472290412302409841950717664641832772206241208918274428499... - Vaclav Kotesovec, Jun 05 2018

From Jianing Song, Nov 30 2019: (Start)

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

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

Maple

a:= proc(n) option remember; `if`(n<0, 0,
      `if`(n=0, 1, n^2 *a(n-1) +a(n-2)))
    end:
seq(a(n), n=1..20);  # Alois P. Heinz, Aug 06 2013

Mathematica

Table[Denominator[FromContinuedFraction[Range[0, n]^2]], {n, 20}] (* Harvey P. Dale, Jul 16 2017 *)

Prog

(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

Crossrefs

Cf. A036245, A073824.

Sequence in context: A339229 A295552 A066998 * A183240 A299715 A377005

Adjacent sequences: A036243 A036244 A036245 * A036247 A036248 A036249

Keyword

frac,nonn

Author

Jeff Burch

Status

approved