A167555 - OEIS

%I #14 Jun 15 2016 13:10:41

%S 2,14,63,209,559,1281,2618,4902,8568,14168,22385,34047,50141,71827,

%T 100452,137564,184926,244530,318611,409661,520443,654005,813694,

%U 1003170,1226420,1487772,1791909,2143883,2549129,3013479,3543176

%N The third left hand column of triangle A167552.

%H G. C. Greubel, <a href="/A167555/b167555.txt">Table of n, a(n) for n = 3..1002</a>

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6, -15, 20, -15, 6, -1).

%F a(n) = (14*n^5 - 115*n^4 + 400*n^3 - 665*n^2 + 486*n - 120)/5!.

%F G.f.: (z^3 + 9*z^2 + 2*z + 2)/(z-1)^6.

%F a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6).

%F a(n) - 5*a(n-1) + 10*a(n-2) - 10*a(n-3) + 5*a(n-4) - a(n-5) = 2*7.

%t LinearRecurrence[{6,-15,20,-15,6,-1},{2,14,63,209,559,1281},40] (* or *) Table[1/120*(66*n+95*n^2+40*n^3+25*n^4+14*n^5),{n,40}] (* _Harvey P. Dale_, Mar 26 2012 *)

%Y Equals the third left hand column of triangle A167552.

%Y Other left hand columns are A005408, A167554, A168302 and A168303.

%K easy,nonn

%O 3,1

%A _Johannes W. Meijer_, Nov 10 2009