A177730 Expansion of (6*x + 1) / ((x - 1)*(2*x - 1)*(4*x - 1)*(8*x - 1)).
1, 21, 245, 2325, 20181, 168021, 1370965, 11075925, 89042261, 714081621, 5719635285, 45785027925, 366392038741, 2931583636821, 23454458533205, 187642826282325, 1501171242849621, 12009484474209621, 96076333921424725, 768612503886583125, 6148907361161794901
Offset: 0
Links
- Muniru A Asiru, Table of n, a(n) for n = 0..200
- Index entries for linear recurrences with constant coefficients, signature (15,-70,120,-64).
Programs
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GAP
a := List([0..200],n->((2^(n+1)-1)^2*(2^(n+2)-1))/3); # Muniru A Asiru, Jan 27 2018
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Maple
a := seq(((2^(n+1)-1)^2 * (2^(n+2)-1))/3, n = 0..200); # Muniru A Asiru, Jan 27 2018
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Mathematica
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 *) -
PARI
Vec((6*x + 1) / ((x - 1)*(2*x - 1)*(4*x - 1)*(8*x - 1)) + O(x^30)) \\ Colin Barker, Jan 27 2018
Formula
From Colin Barker, Jan 27 2018: (Start)
a(n) = ((2^(n+1)-1)^2 * (2^(n+2)-1)) / 3.
a(n) = 15*a(n-1) - 70*a(n-2) + 120*a(n-3) - 64*a(n-4) for n>3.
(End)