A036245 Numerator of fraction equal to the continued fraction [ 0, 1, 4, ..., n^2 ].

1, 4, 37, 596, 14937, 538328, 26393009, 1689690904, 136891356233, 13690825314204, 1656726754374917, 238582343455302252, 40322072770700455505, 7903364845400744581232, 1778297412287938231232705, 455252040910557587940153712, 131569618120563430852935655473

Offset: 1

Author

Jeff Burch

Keywords

• frac
• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..253

Crossrefs

Cf. A036246, A073824.

Programs

Mathematica

Table[Numerator[FromContinuedFraction[Range[0, n]^2]], {n, 1, 20}] (* Vaclav Kotesovec, Aug 14 2021 *)

PARI

A036245(n) = my(v=vector(n+1)); for(i=1, n+1, if(i==1, v[i]=0, 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

Formula

a(n) = n^2 * a(n-1) + a(n-2) for n > 2. - Seiichi Manyama, Jun 05 2018

Lim_{n->oo} a(n)/A036246(n) = A073824. - Jianing Song, Nov 30 2019

a(n) ~ c * n^(2*n + 1) / exp(2*n), where c = 6.5347337470474831902516177263695578212049901774805425962967688345920604685... - Vaclav Kotesovec, Aug 14 2021

Extensions

More terms from Seiichi Manyama, Jun 05 2018