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%I #12 Aug 14 2017 03:00:42
%S 0,3,17,52,121,240,428,707,1102,1641,2355,3278,4447,5902,7686,9845,
%T 12428,15487,19077,23256,28085,33628,39952,47127,55226,64325,74503,
%U 85842,98427,112346,127690,144553,163032,183227,205241,229180,255153
%N Third left hand column of triangle A163940.
%H G. C. Greubel, <a href="/A163943/b163943.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).
%F G.f.: x*(3 + 2*x - 3*x^2 + x^3)/(1-x)^5.
%F a(n)= (2*n + 45*n^2 + 22*n^3 + 3*n^4)/24.
%F a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5).
%F E.g.f.: (1/24)*x*(72 + 132*x + 40*x^2 + 3*x^3)*exp(x). - _G. C. Greubel_, Aug 13 2017
%t LinearRecurrence[{5,-10,10,-5,1},{0,3,17,52,121},40] (* _Harvey P. Dale_, Feb 25 2017 *)
%o (PARI) x='x+O('x^50); concat([0], Vec(x*(3 +2*x -3*x^2 +x^3)/(1-x)^5)) \\ _G. C. Greubel_, Aug 13 2017
%Y Cf. A163972.
%Y Equals the third left hand column of A163940.
%Y A163944 is another left hand column.
%K easy,nonn
%O 0,2
%A _Johannes W. Meijer_, Aug 13 2009
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