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%I #25 Jul 16 2018 10:58:21
%S 1,21,245,2325,20181,168021,1370965,11075925,89042261,714081621,
%T 5719635285,45785027925,366392038741,2931583636821,23454458533205,
%U 187642826282325,1501171242849621,12009484474209621,96076333921424725,768612503886583125,6148907361161794901
%N Expansion of (6*x + 1) / ((x - 1)*(2*x - 1)*(4*x - 1)*(8*x - 1)).
%H Muniru A Asiru, <a href="/A177730/b177730.txt">Table of n, a(n) for n = 0..200</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (15,-70,120,-64).
%F From _Colin Barker_, Jan 27 2018: (Start)
%F a(n) = ((2^(n+1)-1)^2 * (2^(n+2)-1)) / 3.
%F a(n) = 15*a(n-1) - 70*a(n-2) + 120*a(n-3) - 64*a(n-4) for n>3.
%F (End)
%p a := seq(((2^(n+1)-1)^2 * (2^(n+2)-1))/3, n = 0..200); # _Muniru A Asiru_, Jan 27 2018
%t CoefficientList[Series[(6x+1)/((x-1)(2x-1)(4x-1)(8x-1)),{x,0,30}],x] (* or *) LinearRecurrence[{15,-70,120,-64},{1,21,245,2325},30] (* _Harvey P. Dale_, Jul 16 2018 *)
%o (GAP) a := List([0..200],n->((2^(n+1)-1)^2*(2^(n+2)-1))/3); # _Muniru A Asiru_, Jan 27 2018
%o (PARI) Vec((6*x + 1) / ((x - 1)*(2*x - 1)*(4*x - 1)*(8*x - 1)) + O(x^30)) \\ _Colin Barker_, Jan 27 2018
%Y Cf. A006095, A006100.
%K nonn,easy
%O 0,2
%A _Roger L. Bagula_, May 12 2010
%E Heavily edited, with the blessing of _Michel Marcus_ and _Joerg Arndt_, by _Colin Barker_, Jan 27 2018
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