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%I #12 Sep 08 2022 08:45:44
%S 8,17,36,76,160,336,704,1472,3072,6400,13312,27648,57344,118784,
%T 245760,507904,1048576,2162688,4456448,9175040,18874368,38797312,
%U 79691776,163577856,335544320,687865856,1409286144,2885681152,5905580032
%N a(0)=8, a(n) = 2*a(n-1) + 2^(n-1) for n > 0.
%C Diagonal of triangles A062111, A152920.
%H G. C. Greubel, <a href="/A159696/b159696.txt">Table of n, a(n) for n = 0..3300</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (4,-4).
%F a(n) = Sum_{k=0..n} (k+8)*binomial(n,k).
%F From _R. J. Mathar_, Apr 20 2009: (Start)
%F a(n) = (16+n)*2^(n-1).
%F a(n) = 4*a(n-1) - 4*a(n-2).
%F G.f.: (8-15*x)/(1-2*x)^2. (End)
%F E.g.f.: (x+8)*exp(2*x). - _G. C. Greubel_, Jun 02 2018
%e a(0)=8, a(1) = 2*8 + 1 = 17, a(2) = 2*17 + 2 = 36, a(3) = 2*36 + 4 = 76, a(4) = 2*76 + 8 = 160, ...
%t LinearRecurrence[{4,-4}, {8,17}, 30] (* or *) Table[(16+n)*2^(n-1), {n,0,30}] (* _G. C. Greubel_, Jun 02 2018 *)
%o (PARI) for(n=0, 30, print1((16+n)*2^(n-1), ", ")) \\ _G. C. Greubel_, Jun 02 2018
%o (Magma) [(16+n)*2^(n-1): n in [0..30]]; // _G. C. Greubel_, Jun 02 2018
%Y Cf. A000079, A001787, A001792, A045623, A045891, A034007, A111297, A159694, A159695.
%K easy,nonn
%O 0,1
%A _Philippe Deléham_, Apr 20 2009
%E More terms from _R. J. Mathar_, Apr 20 2009
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