This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A191871 #62 Jan 04 2023 02:04:10
%S A191871 0,1,1,9,1,25,9,49,1,81,25,121,9,169,49,225,1,289,81,361,25,441,121,
%T A191871 529,9,625,169,729,49,841,225,961,1,1089,289,1225,81,1369,361,1521,25,
%U A191871 1681,441,1849,121,2025,529,2209,9,2401,625,2601,169,2809,729,3025
%N A191871 a(n) = numerator(n^2 / 2^n).
%C A191871 a(n+1) = largest odd divisor of A000290(n+1). - _Jeremy Gardiner_, Aug 25 2013
%C A191871 In binary, remove all trailing zeros, then square. - _Ralf Stephan_, Aug 26 2013
%C A191871 A fractal sequence. The odd-numbered elements give the odd squares A016754. If these elements are removed, the original sequence is recovered. - _Jeremy Gardiner_, Sep 14 2013
%C A191871 a(n+1) is the denominator of the population variance of the n-th row of Pascal's triangle. - _Chai Wah Wu_, Mar 25 2018
%C A191871 Multiplicative because A000265 is. - _Andrew Howroyd_, Jul 26 2018
%H A191871 Vincenzo Librandi, <a href="/A191871/b191871.txt">Table of n, a(n) for n = 0..5000</a>
%H A191871 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>.
%F A191871 a(n) = A000265(n^2) = A000265(n)^2. - _M. F. Hasler_, Jun 19 2011
%F A191871 Recurrence: a(2n) = a(n), a(2n+1) = (2n+1)^2. - _Ralf Stephan_, Aug 26 2013
%F A191871 From _Amiram Eldar_, Nov 28 2022: (Start)
%F A191871 Multiplicative with a(2^e) = 1, and a(p^e) = p^(2*e) if p > 2.
%F A191871 Sum_{k=1..n} a(k) ~ (4/21) * n^3. (End)
%F A191871 Dirichlet g.f.: zeta(s-2)*(2^s-4)/(2^s-1). - _Amiram Eldar_, Jan 04 2023
%p A191871 [seq(numer(n^2/2^n), n=0..60)]; # _Muniru A Asiru_, Mar 31 2018
%t A191871 a[n_] := Numerator[n^2/2^n]; Table[a[n], {n, 0, 200, 2}]
%o A191871 (PARI) a(n)=(n>>valuation(n,2))^2 \\ _Charles R Greathouse IV_ & _M. F. Hasler_, Jun 19 2011
%o A191871 (Python)
%o A191871 from __future__ import division
%o A191871 def A191871(n):
%o A191871 while not n % 2:
%o A191871 n //= 2
%o A191871 return n**2 # _Chai Wah Wu_, Mar 25 2018
%o A191871 (GAP) List([0..60],n->NumeratorRat(n^2/2^n)); # _Muniru A Asiru_, Mar 31 2018
%Y A191871 Cf. A000265, A000290, A016754.
%K A191871 nonn,frac,easy,mult
%O A191871 0,4
%A A191871 _Vladimir Joseph Stephan Orlovsky_, Jun 18 2011