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A036245
Numerator of fraction equal to the continued fraction [ 0, 1, 4, ..., n^2 ].
10
1, 4, 37, 596, 14937, 538328, 26393009, 1689690904, 136891356233, 13690825314204, 1656726754374917, 238582343455302252, 40322072770700455505, 7903364845400744581232, 1778297412287938231232705, 455252040910557587940153712, 131569618120563430852935655473
OFFSET
1,2
LINKS
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
MATHEMATICA
Table[Numerator[FromContinuedFraction[Range[0, n]^2]], {n, 1, 20}] (* Vaclav Kotesovec, Aug 14 2021 *)
PROG
(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
CROSSREFS
Sequence in context: A377741 A259822 A345102 * A133471 A249607 A097998
KEYWORD
frac,nonn
AUTHOR
EXTENSIONS
More terms from Seiichi Manyama, Jun 05 2018
STATUS
approved