%I #24 Sep 29 2022 11:55:40
%S 1,20,257,2716,25809,230244,1975009,16524332,136058417,1108775668,
%T 8975764161,72350153148,581586939025,4666887733892,37407122372513,
%U 299621333407564,2398809490126833,19199738367402516
%N Expansion of 1 / ((1 - 3*x)*(1 - 4*x)*(1 - 5*x)*(1 - 8*x)).
%H Colin Barker, <a href="/A028027/b028027.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (20,-143,436,-480).
%F a(n) = (8^(n+3) - 10*5^(n+3) + 15*4^(n+3) - 6*3^(n+3))/60. - _Yahia Kahloune_, May 25 2013
%F 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
%F E.g.f.: exp(3*x)*(256*exp(5*x) - 625*exp(2*x) + 480*exp(x) - 81)/30. - _Stefano Spezia_, Sep 29 2022
%t CoefficientList[Series[1/((1 - 3x)(1 - 4x)(1 - 5x)(1 - 8x)) , {x, 0, 29}], x] (* _Alonso del Arte_, Oct 25 2019 *)
%o (PARI) Vec(1 / ((1 - 3*x)*(1 - 4*x)*(1 - 5*x)*(1 - 8*x)) + O(x^20)) \\ _Colin Barker_, Oct 23 2019
%Y Cf. A025986, A028032.
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_