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T(n, 2*n-5), T given by A027960.
3

%I #14 Oct 21 2022 21:40:00

%S 3,7,18,44,98,199,373,654,1085,1719,2620,3864,5540,7751,10615,14266,

%T 18855,24551,31542,40036,50262,62471,76937,93958,113857,136983,163712,

%U 194448,229624,269703,315179,366578,424459,489415,562074,643100,733194,833095,943581,1065470,1199621

%N T(n, 2*n-5), T given by A027960.

%H G. C. Greubel, <a href="/A027967/b027967.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 _Ralf Stephan_, Feb 07 2004: (Start)

%F G.f.: x^3*(3-2*x)*(1-3*x+5*x^2-3*x^3+x^4)/(1-x)^6.

%F Differences of A027968. (End)

%F From _G. C. Greubel_, Jun 30 2019: (Start)

%F a(n) = (840 - 736*n + 300*n^2 - 45*n^3 + n^5)/120.

%F E.g.f.: (-120*(7 + 3*x + x^2) + (840 - 480*x + 180*x^2 - 20*x^3 + 10*x^4 + x^5)*exp(x))/120. (End)

%t LinearRecurrence[{6,-15,20,-15,6,-1}, {3,7,18,44,98,199}, 50] (* _G. C. Greubel_, Jun 30 2019 *)

%o (PARI) for(n=3,50, print1((840-736*n+300*n^2-45*n^3+n^5)/120, ", ")) \\ _G. C. Greubel_, Jun 30 2019

%o (Magma) [(840-736*n+300*n^2-45*n^3+n^5)/120: n in [3..50]]; // _G. C. Greubel_, Jun 30 2019

%o (Sage) [(840-736*n+300*n^2-45*n^3+n^5)/120 for n in (3..50)] # _G. C. Greubel_, Jun 30 2019

%o (GAP) List([3..50], n-> (840-736*n+300*n^2-45*n^3+n^5)/120) _G. C. Greubel_, Jun 30 2019

%Y A column of triangle A027011.

%K nonn,easy

%O 3,1

%A _Clark Kimberling_

%E Terms a(37) onward added by _G. C. Greubel_, Jun 30 2019