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%I #39 Sep 08 2022 08:45:02
%S 33,492,2055,5898,13797,28248,52587,91110,149193,233412,351663,513282,
%T 729165,1011888,1375827,1837278,2414577,3128220,4000983,5058042,
%U 6327093,7838472,9625275,11723478,14172057,17013108,20291967,24057330
%N Row 5 of A007754.
%C a(n) is divisible by n+3.
%H Seiichi Manyama, <a href="/A058796/b058796.txt">Table of n, a(n) for n = 0..10000</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 _Colin Barker_, Jan 16 2013: (Start)
%F a(n) = 33 + 173*n + 189*n^2 + 81*n^3 + 15*n^4 + n^5.
%F a(n) = (n + 3)*(n^4 + 12*n^3 + 45*n^2 + 54*n + 11).
%F G.f.: 3*(6*x^5 - 37*x^4 + 96*x^3 - 134*x^2 + 98*x + 11) / (x-1)^6.
%F (End)
%F E.g.f.: (33 + 459*x + 552*x^2 + 196*x^3 + 25*x^4 + x^5)*exp(x). - _G. C. Greubel_, Nov 29 2018
%p seq(coeff(series(3*(6*x^5-37*x^4+96*x^3-134*x^2+98*x+11)/(1-x)^6,x,n+1), x, n), n = 0 .. 30); # _Muniru A Asiru_, Nov 30 2018
%t LinearRecurrence[{6, -15, 20, -15, 6, -1}, {33, 492, 2055, 5898, 13797, 28248}, 30] (* _Vincenzo Librandi_, Sep 22 2016 *)
%o (Magma) [33+173*n+189*n^2+81*n^3+15*n^4+n^5: n in [0..40]]; // _Vincenzo Librandi_, Sep 22 2016
%o (PARI) vector(40, n, n--; 33 +173*n +189*n^2 +81*n^3 +15*n^4 +n^5) \\ _G. C. Greubel_, Nov 29 2018
%o (Sage) [(33 +173*n +189*n^2 +81*n^3 +15*n^4 +n^5) for n in range(40)] # _G. C. Greubel_, Nov 29 2018
%o (GAP) List([0..40], n -> 33+173*n+189*n^2+81*n^3+15*n^4+n^5); # _G. C. Greubel_, Nov 29 2018
%o (Python) for n in range(0, 40): print(33+173*n+189*n**2+81*n**3+15*n**4+n**5, end=', ') # _Stefano Spezia_, Nov 30 2018
%Y Cf. A007754.
%K nonn,easy
%O 0,1
%A _Christian G. Bower_, Dec 02 2000
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