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%I #31 Feb 05 2022 14:58:36
%S 0,2,7,19,47,111,255,575,1279,2815,6143,13311,28671,61439,131071,
%T 278527,589823,1245183,2621439,5505023,11534335,24117247,50331647,
%U 104857599,218103807,452984831,939524095
%N a(n) = (n+3)*2^n - 1.
%C Binomial transform of [2/1, 3/2, 4/3, 5/4, ...] = 2/1, 7/2, 19/3, 47/4, 111/5, ... - _Gary W. Adamson_, Apr 28 2005
%C Binomial transform of A087156 := [0,2,3,4,5,6,7,8,9,10,...]. - _Philippe Deléham_, Nov 25 2008
%C Partial sums of A045623 minus 1. - _R. J. Mathar_, Jan 25 2009
%C For n >= 0: sums of rows of the triangle in A173786. - _Reinhard Zumkeller_, Feb 28 2010
%D W. A. Whitworth, DCC Exercises in Choice and Chance, Stechert, NY, 1945, p. 28.
%H G. C. Greubel, <a href="/A006589/b006589.txt">Table of n, a(n) for n = -1..1000</a>
%H M. Le Brun, <a href="/A006577/a006577.pdf">Email to N. J. A. Sloane, Jul 1991</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (5,-8,4).
%F From _R. J. Mathar_, Jan 25 2009: (Start)
%F G.f.: (2-3*x)/((1-x)*(1-2*x)^2).
%F a(n) = 5*a(n-1) - 8*a(n-2) + 4*a(n-3). (End)
%F a(n) = A001792(n+1) - 1. - _R. J. Mathar_, Aug 03 2015
%F a(n) = Sum_{k=0..n} Sum_{i=0..n} (binomial(n,i) + binomial(k,i)). - _Wesley Ivan Hurt_, Sep 21 2017
%F E.g.f.: (3 + 2*x)*exp(2*x) - exp(x). - _G. C. Greubel_, Jul 07 2021
%t Table[2^n*(n+3) -1, {n,-1,30}] (* _G. C. Greubel_, Jul 07 2021 *)
%o (PARI) a(n)=(n+3)*2^n-1 \\ _Charles R Greathouse IV_, Oct 07 2015
%o (Sage) [2^n*(n+3) -1 for n in (-1..30)] # _G. C. Greubel_, Jul 07 2021
%Y Cf. A001792, A045623, A173786.
%K nonn,easy
%O -1,2
%A _N. J. A. Sloane_
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