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%I #20 Aug 14 2021 03:42:52
%S 1,4,37,596,14937,538328,26393009,1689690904,136891356233,
%T 13690825314204,1656726754374917,238582343455302252,
%U 40322072770700455505,7903364845400744581232,1778297412287938231232705,455252040910557587940153712,131569618120563430852935655473
%N Numerator of fraction equal to the continued fraction [ 0, 1, 4, ..., n^2 ].
%H Seiichi Manyama, <a href="/A036245/b036245.txt">Table of n, a(n) for n = 1..253</a>
%F a(n) = n^2 * a(n-1) + a(n-2) for n > 2. - _Seiichi Manyama_, Jun 05 2018
%F Lim_{n->oo} a(n)/A036246(n) = A073824. - _Jianing Song_, Nov 30 2019
%F a(n) ~ c * n^(2*n + 1) / exp(2*n), where c = 6.5347337470474831902516177263695578212049901774805425962967688345920604685... - _Vaclav Kotesovec_, Aug 14 2021
%t Table[Numerator[FromContinuedFraction[Range[0, n]^2]], {n, 1, 20}] (* _Vaclav Kotesovec_, Aug 14 2021 *)
%o (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
%Y Cf. A036246, A073824.
%K frac,nonn
%O 1,2
%A _Jeff Burch_
%E More terms from _Seiichi Manyama_, Jun 05 2018
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