%I #15 Sep 26 2015 18:35:20
%S 0,1,6,21,56,127,259,490,876,1498,2472,3963,6204,9522,14374,21397,
%T 31477,45844,66203,94915,135247,191717,270570,380435,533232,745424,
%U 1039745,1447585,2012282,2793666,3874331,5368292,7432934,10285505,14225881,19667988,27183173
%N Expansion of x/((1 - x - x^4)*(1 - x)^5).
%C The coefficients of the recursion for a(n) are given by the 6th row of A145152.
%H Vincenzo Librandi, <a href="/A145134/b145134.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (6, -15, 20, -14, 1, 9, -10, 5, -1).
%F a(n) = 6a(n-1) -15a(n-2) +20a(n-3) -14a(n-4) +a(n-5) +9a(n-6) -10a(n-7) +5a(n-8) -a(n-9).
%p col:= proc(k) local l, j, M, n; l:= `if` (k=0, [1, 0, 0, 1], [seq (coeff ( -(1-x-x^4) *(1-x)^(k-1), x, j), j=1..k+3)]); M:= Matrix (nops(l), (i,j)-> if i=j-1 then 1 elif j=1 then l[i] else 0 fi); `if` (k=0, n->(M^n)[2,3], n->(M^n)[1,2]) end: a:= col(6): seq(a(n), n=0..40);
%t CoefficientList[Series[x / ((1 - x - x^4) (1 - x)^5), {x, 0, 40}], x] (* _Vincenzo Librandi_, Jun 06 2013 *)
%t LinearRecurrence[{6,-15,20,-14,1,9,-10,5,-1},{0,1,6,21,56,127,259,490,876},40] (* _Harvey P. Dale_, Aug 14 2013 *)
%o (PARI) concat(0,Vec(1/(1-x-x^4)/(1-x)^5+O(x^99))) \\ _Charles R Greathouse IV_, Sep 25 2012
%Y 6th column of A145153. Cf. A145152.
%K nonn,easy
%O 0,3
%A _Alois P. Heinz_, Oct 03 2008