%I #12 Mar 03 2024 15:58:06
%S 24,368,2736,13712,53121,171258,480711,1210572,2793219,5996562,
%T 12117677,23257104,42696758,75408396,128723898,213203256,343741122,
%U 540958044,832928118,1257300704,1863880095,2717733590,3902905305,5526820260,7725470805
%N The fifth left hand column of triangle A167565.
%H G. C. Greubel, <a href="/A168304/b168304.txt">Table of n, a(n) for n = 5..1000</a>
%H <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (10, -45, 120, -210, 252, -210, 120, -45, 10, -1).
%F a(n) = (321*n^9 - 4500*n^8 + 25506*n^7 - 75096*n^6 + 121905*n^5 - 104580*n^4 + 2736*n^2 + 37164*n^3 - 3456*n)/9!.
%F G.f.: (z^4 + 32*z^3 + 136*z^2 + 128*z + 24)/(1-z)^10.
%F a(n) = 10*a(n-1) - 45*a(n-2) + 120*a(n-3) - 210*a(n-4) + 252*a(n-5) - 210*a(n-6) + 120*a(n-7) - 45*a(n-8) + 10*a(n-9) - a(n-10).
%F a(n) - 9*a(n-1) + 36*a(n-2) - 84*a(n-3) + 126*a(n-4) - 126*a(n-5) + 84*a(n-6) - 36*a(n-7) + 9*a(n-8) - a(n-9) = 321.
%t LinearRecurrence[{10,-45,120,-210,252,-210,120,-45,10,-1},{24, 368, 2736, 13712, 53121, 171258, 480711, 1210572, 2793219, 5996562},50] (* _G. C. Greubel_, Jul 17 2016 *)
%o (Magma) [(321*n^9-4500*n^8+25506*n^7-75096*n^6+121905*n^5- 104580*n^4+2736*n^2+37164*n^3-3456*n)/362880: n in [5..40]]; // _Vincenzo Librandi_, Jul 18 2016
%Y Equals the fifth left hand column of triangle A167565.
%Y Other left hand columns are A000027, A000292, A167566 and A167567.
%K easy,nonn
%O 5,1
%A _Johannes W. Meijer_, Nov 23 2009