A299335 - OEIS

%I #13 Feb 13 2018 04:09:11

%S 1,5,17,45,103,211,399,707,1190,1918,2982,4494,6594,9450,13266,18282,

%T 24783,33099,43615,56771,73073,93093,117481,146965,182364,224588,

%U 274652,333676,402900,483684,577524,686052,811053,954465,1118397,1305129,1517131,1757063

%N Expansion of 1 / ((1 - x)^7*(1 + x)^2).

%H Colin Barker, <a href="/A299335/b299335.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 (5,-8,0,14,-14,0,8,-5,1).

%F a(n) = (2*n^6 + 54*n^5 + 575*n^4 + 3060*n^3 + 8468*n^2 + 11376*n + 5760) / 5760 for n even.

%F a(n) = (2*n^6 + 54*n^5 + 575*n^4 + 3060*n^3 + 8468*n^2 + 11286*n + 5355) / 5760 for n odd.

%F a(n) = 5*a(n-1) - 8*a(n-2) + 14*a(n-4) - 14*a(n-5) + 8*a(n-7) - 5*a(n-8) + a(n-9) for n>8.

%t CoefficientList[Series[1/((1 - x)^7 (1 + x)^2), {x, 0, 40}], x] (* or *) LinearRecurrence[{5, -8, 0, 14, -14, 0, 8, -5, 1}, {1, 5, 17, 45, 103, 211, 399, 707, 1190}, 41] (* _Robert G. Wilson v_, Feb 07 2018 *)

%o (PARI) Vec(1 / ((1 - x)^7*(1 + x)^2) + O(x^40))

%Y Cf. A001769, A060099, A299336, A299337, A299338.

%K nonn,easy

%O 0,2

%A _Colin Barker_, Feb 07 2018