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A036296 Denominator of Sum_{i=1..n} i/2^i.

%I A036296 #46 Jan 05 2025 19:51:35
%S A036296 1,2,1,8,8,32,8,128,128,512,256,2048,2048,8192,1024,32768,32768,
%T A036296 131072,65536,524288,524288,2097152,524288,8388608,8388608,33554432,
%U A036296 16777216,134217728,134217728,536870912,33554432,2147483648,2147483648,8589934592,4294967296
%N A036296 Denominator of Sum_{i=1..n} i/2^i.
%C A036296 Sum_{i>=0} i/2^i = 2. - _Alonso del Arte_, Aug 15 2012
%D A036296 C. C. Clawson, The Beauty and Magic of Numbers. New York: Plenum Press (1996): 95.
%H A036296 Colin Barker, <a href="/A036296/b036296.txt">Table of n, a(n) for n = 0..1000</a>
%H A036296 A. F. Horadam, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Scanned/12-3/horadam.pdf">Oresme numbers</a>, Fib. Quart., 12 (1974), 267-271.
%F A036296 a(n) = denominator(2-(n+2)/2^n). - _Sean A. Irvine_, Oct 25 2020
%F A036296 a(n) = A000079(n)/A006519(n+2), for n>=1. - _Ridouane Oudra_, Jul 16 2023
%F A036296 Denominators of coefficients in expansion of 2*x / ((1 - x) * (2 - x)^2). - _Ilya Gutkovskiy_, Aug 04 2023
%e A036296 a(4) = 8 because 1/2 + 2/4 + 3/8 + 4/16 = 1/2 + 1/2 + 3/8 + 1/4 = 1 + 5/8 = 13/8.
%p A036296 seq(denom(2-(n+2)/2^n), n=0..50); # _Ridouane Oudra_, Jul 16 2023
%t A036296 Table[Denominator[Sum[i/2^i, {i, n}]], {n, 40}] (* _Alonso del Arte_, Aug 08 2012 *)
%o A036296 (PARI) concat(1, vector(100, n, denominator(sum(i=1, n, i/2^i)))) \\ _Colin Barker_, Nov 09 2014
%o A036296 (PARI) a(n) = denominator(2-(n+2)/2^n); \\ _Joerg Arndt_, Jul 17 2023
%o A036296 (Magma) [1] cat [Denominator(&+[i/2^i: i in [1..n]]): n in [1..40]]; // _Vincenzo Librandi_, Nov 09 2014
%Y A036296 Cf. A036295 (numerators).
%Y A036296 Cf. A000079, A006519.
%K A036296 nonn,frac,easy
%O A036296 0,2
%A A036296 _N. J. A. Sloane_