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%I #27 Sep 08 2022 08:46:20
%S 1,16,94,331,871,1906,3676,6469,10621,16516,24586,35311,49219,66886,
%T 88936,116041,148921,188344,235126,290131,354271,428506,513844,611341,
%U 722101,847276,988066,1145719,1321531,1516846,1733056,1971601,2233969,2521696,2836366
%N Expansion of (1+11*x+24*x^2+11*x^3+x^4)/(1-x)^5.
%H Robert Israel, <a href="/A294433/b294433.txt">Table of n, a(n) for n = 0..10000</a>
%H J. A. De Loera, D. C. Haws and M. Koppe, <a href="http://arxiv.org/abs/0710.4346">Ehrhart Polynomials of Matroid Polytopes and Polymatroids</a>, arXiv:0710.4346 [math.CO], 2007; Discrete Comput. Geom., 42 (2009), 670-702. See Table 2.
%H J. A. De Loera, D. C. Haws and M. Koppe, <a href="http://arxiv.org/abs/0710.4346">Ehrhart Polynomials of Matroid Polytopes and Polymatroids</a>, arXiv:0710.4346 [math.CO], 2007; Discrete Comput. Geom., 42 (2009), 670-702.
%H D. C. Haws, <a href="http://www.math.ucdavis.edu/~haws/Matroids/">Matroids</a> [Broken link, Oct 30 2017]
%H D. C. Haws, <a href="https://www.math.ucdavis.edu/~mkoeppe/art/Matroids/">Matroids</a> [Copy on website of Matthias Koeppe]
%H D. C. Haws, <a href="/A160747/a160747.pdf">Matroids/a> [Cached copy, pdf file only]
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).
%F a(n) = 1 + 7*n/2 + 11*n^2/2 + 4*n^3 + 2*n^4. - _Robert Israel_, Oct 30 2017
%F From _Colin Barker_, Oct 31 2017: (Start)
%F G.f.: (1 + 11*x + 24*x^2 + 11*x^3 + x^4) / (1 - x)^5.
%F a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>4.
%F (End)
%p seq(1 + 7*n/2 + 11*n^2/2 + 4*n^3 + 2*n^4,n=0..30); # _Robert Israel_, Oct 30 2017
%t Table[1 + 7*n/2 + 11*n^2/2 + 4*n^3 + 2*n^4, {n, 0, 30}] (* or *) LinearRecurrence[{5,-10,10,-5,1}, {1, 16, 94, 331, 871}, 30] (* _G. C. Greubel_, Apr 29 2018 *)
%o (PARI) Vec((1 + 11*x + 24*x^2 + 11*x^3 + x^4) / (1 - x)^5 + O(x^40)) \\ _Colin Barker_, Oct 31 2017
%o (PARI) a(n) = my(t=n*(n+1)/2); 8*t^2+7*t+1; \\ _Altug Alkan_, Apr 30 2018
%o (Magma) [1 + 7*n/2 + 11*n^2/2 + 4*n^3 + 2*n^4: n in [0..30]]; // _G. C. Greubel_, Apr 29 2018
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_, Oct 30 2017
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