A299335 Expansion of 1 / ((1 - x)^7*(1 + x)^2).

1, 5, 17, 45, 103, 211, 399, 707, 1190, 1918, 2982, 4494, 6594, 9450, 13266, 18282, 24783, 33099, 43615, 56771, 73073, 93093, 117481, 146965, 182364, 224588, 274652, 333676, 402900, 483684, 577524, 686052, 811053, 954465, 1118397, 1305129, 1517131, 1757063

Offset: 0

Author

Colin Barker, Feb 07 2018

Keywords

• nonn
• easy

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (5,-8,0,14,-14,0,8,-5,1).

Crossrefs

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

Programs

Mathematica

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 *)

PARI

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

Formula

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

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

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.