A028027 Expansion of 1 / ((1 - 3*x)*(1 - 4*x)*(1 - 5*x)*(1 - 8*x)).

1, 20, 257, 2716, 25809, 230244, 1975009, 16524332, 136058417, 1108775668, 8975764161, 72350153148, 581586939025, 4666887733892, 37407122372513, 299621333407564, 2398809490126833, 19199738367402516

Offset

0,2

Links

Colin Barker, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (20,-143,436,-480).

Formula

a(n) = (8^(n+3) - 10*5^(n+3) + 15*4^(n+3) - 6*3^(n+3))/60. - Yahia Kahloune, May 25 2013

a(n) = 20*a(n-1) - 143*a(n-2) + 436*a(n-3) - 480*a(n-4) for n > 3. - Colin Barker, Oct 23 2019

E.g.f.: exp(3*x)*(256*exp(5*x) - 625*exp(2*x) + 480*exp(x) - 81)/30. - Stefano Spezia, Sep 29 2022

Mathematica

CoefficientList[Series[1/((1 - 3x)(1 - 4x)(1 - 5x)(1 - 8x)) , {x, 0, 29}], x] (* Alonso del Arte, Oct 25 2019 *)

Prog

(PARI) Vec(1 / ((1 - 3*x)*(1 - 4*x)*(1 - 5*x)*(1 - 8*x)) + O(x^20)) \\ Colin Barker, Oct 23 2019

Crossrefs

Cf. A025986, A028032.

Sequence in context: A028032 A348055 A025986 * A268764 A081244 A025966

Adjacent sequences: A028024 A028025 A028026 * A028028 A028029 A028030

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved