cp's OEIS Frontend

A048470 a(n) = (n+1)*(2^(n+1) - n)/2.

%I A048470 #24 Sep 08 2022 08:44:57
%S A048470 1,3,9,26,70,177,427,996,2268,5075,11209,24510,53170,114597,245655,
%T A048470 524168,1113976,2359143,4980565,10485570,22019886,46137113,96468739,
%U A048470 201326316,419430100,872414907,1811938977,3758096006,7784627818
%N A048470 a(n) = (n+1)*(2^(n+1) - n)/2.
%C A048470 a(n) = T(0,n) + T(1,n-1) + ... + T(n,0), array T given by A047858.
%C A048470 Sum of the consecutive integers from 2^n-n up to and including 2^n. - _J. M. Bergot_, Jun 27 2013
%H A048470 Vincenzo Librandi, <a href="/A048470/b048470.txt">Table of n, a(n) for n = 0..1000</a>
%F A048470 G.f.: (-1 + 5*x^3 - 7*x^2 + 4*x)/((2*x-1)^2*(x-1)^3). - Maksym Voznyy (voznyy(AT)mail.ru), Aug 13 2009
%F A048470 a(n) = 3^n - Eulerian(n,2) = A000244(n) - A000460(n). - _Peter Luschny_, May 13 2016
%o A048470 (Magma) [(n+1)*(2^(n+1)-n)/2: n in [0..30]]; // _Vincenzo Librandi_, Sep 23 2011
%o A048470 (PARI) a(n)=(n+1)*(2<<n-n)/2 \\ _Charles R Greathouse IV_, Jun 28 2013
%K A048470 nonn,easy
%O A048470 0,2
%A A048470 _Clark Kimberling_
%E A048470 Edited by _T. D. Noe_, Dec 11 2006