%I #22 Mar 19 2018 21:39:06
%S 1,25,419,5885,74811,892605,10199659,113009005,1223954171,13030808285,
%T 136920690699,1424085096525,14693717768731,150657001125565,
%U 1537006821834539,15618310264486445,158202271944562491
%N Expansion of 1/((1-7x)(1-8x)(1-10x)).
%H Muniru A Asiru, <a href="/A020838/b020838.txt">Table of n, a(n) for n = 0..200</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (25,-206,560).
%F a(n) = 25*a(n-1) - 206*a(n-2) + 560*a(n-3), n >= 3. - _Vincenzo Librandi_, Mar 15 2011
%F a(n) = 18*a(n-1) - 80*a(n-2) + 7^n, n >= 2. - _Vincenzo Librandi_, Mar 15 2011
%F a(n) = 7^(n+2)/3 + 5*10^(n+1)/3 - 4*8^(n+1). - _R. J. Mathar_, Mar 15 2011
%p [seq(coeftayl(1/((1-7*x)*(1-8*x)*(1-10*x)), x = 0, k), k=1..20)]; # _Muniru A Asiru_, Mar 19 2018
%t Table[SeriesCoefficient[1/((1 - 7x)(1 - 8x)(1 - 10x)), {x, 0, n}], {n, 0, 19}] (* _Alonso del Arte_, Mar 19 2018 *)
%o (PARI) x='x+O('x^99); Vec(1/((1-7*x)*(1-8*x)*(1-10*x))) \\ _Altug Alkan_, Mar 19 2018
%o (GAP) a:=[1,25,419];; for n in [4..20] do a[n]:=25*a[n-1]-206*a[n-2]+560*a[n-3]; od; a; # _Muniru A Asiru_, Mar 19 2018
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_