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%I #18 Sep 08 2022 08:46:09
%S 1,5,21,84,331,1300,5111,20144,79611,315420,1252351,4980904,19837091,
%T 79086740,315557991,1259856864,5032285771,20107685260,80366302031,
%U 321271760024,1284506433651,5136283390980,20539905484471,82143935602384,328528679208731,1313973518843900,5255470464625311,21020610992695944
%N Expansion of (1-5*x+6*x^2-x^3)/((1-x)*(1-2*x)*(1-3*x)*(1-4*x)).
%H Todd Silvestri, <a href="/A246986/b246986.txt">Table of n, a(n) for n = 0..1660</a>
%H A. Prasad, <a href="http://arxiv.org/abs/1407.5284">Equivalence classes of nodes in trees and rational generating functions</a>, arXiv:1407.5284 [math.CO], 2014.
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (10,-35,50,-24).
%F a(n) = (3^(n+1)+7*4^n-3*2^n-1)/6. - _Todd Silvestri_, Nov 16 2014
%t a[n_Integer/;n>=0]:=(3^(n+1)+7*4^n-3*2^n-1)/6 (* _Todd Silvestri_, Nov 16 2014 *)
%t CoefficientList[Series[(1 - 5 t + 6 t^2 - t^3) / ((1 - t) (1 - 2 t) (1 - 3 t) (1 - 4 t)), {t, 0, 40}], t] (* _Vincenzo Librandi_, Nov 16 2014 *)
%t LinearRecurrence[{10,-35,50,-24},{1,5,21,84},30] (* _Harvey P. Dale_, May 12 2017 *)
%o (Magma) [(3^(n+1)+7*4^n-3*2^n-1)/6: n in [0..30]]; // _Vincenzo Librandi_, Nov 16 2014
%o (PARI) Vec((1-5*x+6*x^2-x^3)/((1-x)*(1-2*x)*(1-3*x)*(1-4*x)) + O(x^30)) \\ _Michel Marcus_, Jan 14 2016
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_, Sep 15 2014