%I #11 Mar 03 2024 17:45:28

%S -60,-768,-5008,-20672,-46720,76800,1540608,10610688,55114752,

%T 246005760,992808960,3720331264,13156941824,44395134976,144054681600,

%U 452151214080,1379061202944,4102054477824,11934819680256,34047283691520,95430020956160,263252302888960

%N The fourth left hand column of triangle A167591.

%H G. C. Greubel, <a href="/A168307/b168307.txt">Table of n, a(n) for n = 4..1000</a>

%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (16, -112, 448, -1120, 1792, -1792, 1024, -256).

%F a(n) = 2^n*(27*n^7 - 434*n^6 + 2289*n^5 - 5705*n^4 + 7938*n^3 - 6461*n^2 + 2346*n)/10080.

%F G.f.: (320*z^3 + 560*z^2 + 192*z - 60)/(1-2*z)^8.

%F a(n) = 16*a(n-1) - 112*a(n-2) + 448*a(n-3) - 1120*a(n-4) + 1792*a(n-5) - 1792*a(n-6) + 1024*a(n-7) - 256*a(n-8).

%F a(n) - 15*a(n-1) + 98*a(n-2) - 364*a(n-3) + 840*a(n-4) - 1232*a(n-5) + 1120*a(n-6) - 576*a(n-7) + 128*a(n-8) = 27*2^(n-2).

%t LinearRecurrence[{16,-112,448,-1120,1792,-1792,1024,-256}, {-60, -768, -5008, -20672, -46720, 76800, 1540608, 10610688}, 50] (* _G. C. Greubel_, Jul 17 2016 *)

%o (Magma) [2^n*(27*n^7-434*n^6+2289*n^5-5705*n^4+7938*n^3- 6461*n^2+2346*n)/10080: n in [4..30]]; // _Vincenzo Librandi_, Jul 18 2016

%Y Equals the fourth left hand column of triangle A167591.

%Y Other left hand columns are A001787, A167592, A167593 and A168308.

%K easy,sign

%O 4,1

%A _Johannes W. Meijer_, Nov 23 2009, Nov 25 2009