A146523 - OEIS

%I #28 Feb 21 2023 07:31:43

%S 1,5,10,20,40,80,160,320,640,1280,2560,5120,10240,20480,40960,81920,

%T 163840,327680,655360,1310720,2621440,5242880,10485760,20971520,

%U 41943040,83886080,167772160,335544320,671088640,1342177280,2684354560,5368709120,10737418240

%N Binomial transform of A010685.

%C Linked to A029609 by a Catalan transform.

%C Hankel transform is (1, -15, 0, 0, 0, 0, 0, 0, 0, ...).

%H G. C. Greubel, <a href="/A146523/b146523.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (2).

%F a(n) = 5*2^(n-1) for n >= 1, a(0) = 1.

%F a(n) = Sum_{k=0..n} A109466(n,k)*A029609(k).

%F a(n) = A084215(n+1) = A020714(n-1), n > 0. - _R. J. Mathar_, Nov 02 2008

%F G.f.: (1 + 3*x)/(1 - 2*x). - _Vladimir Joseph Stephan Orlovsky_, Jun 21 2011

%F G.f.: G(0), where G(k)= 1 + 3*x/(1 -  2*x/(2*x + 3*x/G(k+1) )); (continued fraction). - _Sergei N. Gladkovskii_, Jul 03 2013

%F E.g.f.: (5*exp(2*x) - 3)/2. - _Stefano Spezia_, Feb 20 2023

%t CoefficientList[Series[(1+3x)/(1-2x), {x,0,50}], x] (* _Vladimir Joseph Stephan Orlovsky_, Jun 21 2011 *)

%t Join[{1}, 5*2^(Range[40] -1)] (* _G. C. Greubel_, Nov 23 2021 *)

%o (PARI) a(n)=if(n,5<<(n-1),1) \\ _Charles R Greathouse IV_, Jan 17 2012

%o (Sage) [1]+[5*2^(n-1) for n in (1..50)] # _G. C. Greubel_, Nov 23 2021

%Y Cf. A010685, A020714, A029609, A084215, A109466.

%K nonn,easy

%O 0,2

%A _Philippe Deléham_, Oct 30 2008