A021764 Expansion of 1/((1-x)(1-4x)(1-5x)(1-8x)).

1, 18, 215, 2160, 19821, 172638, 1456915, 12056220, 98541641, 799142058, 6448579215, 51871439880, 416407919461, 3338534836278, 26744994007115, 214144960297140, 1714090450201281, 13717400347223298, 109762678131820615

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Index entries for linear recurrences with constant coefficients, signature (18,-109,252,-160).

Formula

G.f.: 1/((1-x)*(1-4*x)*(1-5*x)*(1-8*x)).

a(n) = -1/84 +4^(n+2)/3 -5^(n+3)/12 +2^(3n+7)/21. - Bruno Berselli, May 07 2013

a(n) = 18*a(n-1) - 109*a(n-2) + 252*a(n-3) - 160*a(n-4). - Wesley Ivan Hurt, May 17 2023

Mathematica

CoefficientList[Series[1/((1 - x) (1 - 4 x) (1 - 5 x) (1 - 8 x)), {x, 0, 20}], x] (* Bruno Berselli, May 07 2013 *)
LinearRecurrence[{18, -109, 252, -160}, {1, 18, 215, 2160}, 30] (* Harvey P. Dale, Jul 28 2015 *)

Prog

(PARI) Vec(1/((1-x)*(1-4*x)*(1-5*x)*(1-8*x))+O(x^20)) \\ Bruno Berselli, May 07 2013
(Magma) m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-4*x)*(1-5*x)*(1-8*x)))); // Bruno Berselli, May 07 2013

Crossrefs

Cf. A018250 (first differences).

Sequence in context: A025932 A260569 A125430 * A059357 A324638 A009470

Adjacent sequences: A021761 A021762 A021763 * A021765 A021766 A021767

Keyword

nonn,easy

Author

N. J. A. Sloane.

Status

approved