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A167566 The third left hand column of triangle A167565. 4

%I

%S 2,16,67,202,497,1064,2058,3684,6204,9944,15301,22750,32851,46256,

%T 63716,86088,114342,149568,192983,245938,309925,386584,477710,585260,

%U 711360,858312,1028601,1224902,1450087,1707232,1999624,2330768,2704394

%N The third left hand column of triangle A167565.

%H G. C. Greubel, <a href="/A167566/b167566.txt">Table of n, a(n) for n = 3..1000</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 From _Johannes W. Meijer_, Nov 23 2009: (Start)

%F a(n) = (7*n^5 - 30*n^4 + 45*n^3 - 30*n^2 + 8*n)/5!.

%F G.f.: (1*z^2 + 4*z + 2)/(1-z)^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) = 7. (End)

%F a(n) = A024166(n-2) + A000389(n+2). - _J. M. Bergot_, Jul 04 2017

%t Table[(7*n^5 - 30*n^4 + 45*n^3 - 30*n^2 + 8*n)/5!, {n,3,100}] (* or *) LinearRecurrence[{6,-15,20,-15,6,-1}, {2, 16, 67, 202, 497, 1064}, 100] (* _G. C. Greubel_, Jun 16 2016 *)

%o (PARI) Vec((1*z^2 + 4*z + 2)/(1-z)^6 + O(z^50)) \\ _Michel Marcus_, Jul 05 2017

%o (PARI) a(n) = n*(7*n^4 - 30*n^3 + 45*n^2 - 30*n + 8)/120 \\ _Charles R Greathouse IV_, Jul 14 2017

%Y Equals the third left hand column of triangle A167565.

%Y Other left hand columns are A000027, A000292, A167567 and A168304.

%K easy,nonn

%O 3,1

%A _Johannes W. Meijer_, Nov 10 2009

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Last modified August 6 14:33 EDT 2020. Contains 336246 sequences. (Running on oeis4.)