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

0,2

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).

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)

Maple

a := seq(((2^(n+1)-1)^2 * (2^(n+2)-1))/3, n = 0..200); # Muniru A Asiru, Jan 27 2018

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 *)

Prog

(GAP) a := List([0..200], n->((2^(n+1)-1)^2*(2^(n+2)-1))/3); # Muniru A Asiru, Jan 27 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

Crossrefs

Cf. A006095, A006100.

Sequence in context: A175843 A198974 A271792 * A199300 A302992 A344919

Adjacent sequences: A177727 A177728 A177729 * A177731 A177732 A177733

Keyword

nonn,easy

Author

Roger L. Bagula, May 12 2010

Extensions

Heavily edited, with the blessing of Michel Marcus and Joerg Arndt, by Colin Barker, Jan 27 2018

Status

approved