%I #11 Mar 03 2024 17:43:11
%S -15,-48,2024,31616,274480,1784320,9645312,45735936,196441344,
%T 780595200,2912532480,10315202560,34963222528,114140905472,
%U 360716042240,1108051230720,3319564664832,9726122262528,27935264735232,78810426900480,218761889054720,598349308755968
%N The fourth left hand column of triangle A167580.
%H G. C. Greubel, <a href="/A168305/b168305.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*(54*n^7 - 763*n^6 + 4158*n^5 - 11305*n^4 + 16401*n^3 - 12502*n^2 + 4587*n - 630)/10080.
%F G.f.: (16*z^4 + 576*z^3 + 1112*z^2 + 192*z - 15)/(2*z-1)^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-1).
%t LinearRecurrence[{16, -112, 448, -1120, 1792, -1792, 1024, -256}, {-15, -48, 2024, 31616, 274480, 1784320, 9645312, 45735936}, 997] (* _G. C. Greubel_, Jul 17 2016 *)
%o (Magma) [2^n*(54*n^7-763*n^6+4158*n^5-11305*n^4+16401*n^3- 12502*n^2+4587*n-630)/10080: n in [4..40]]; // _Vincenzo Librandi_, Jul 18 2016
%Y Equals the fourth left hand column of triangle A167580.
%Y Other left hand columns are A014480, A167581, A167582 and A168306.
%K easy,sign
%O 4,1
%A _Johannes W. Meijer_, Nov 23 2009