A160750 Expansion of (1+11*x+24*x^2+11*x^3+10*x^4)/(1-x)^5.
1, 16, 94, 331, 880, 1951, 3811, 6784, 11251, 17650, 26476, 38281, 53674, 73321, 97945, 128326, 165301, 209764, 262666, 325015, 397876, 482371, 579679, 691036, 817735, 961126, 1122616, 1303669, 1505806, 1730605, 1979701, 2254786, 2557609
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..10000
- J. A. De Loera, D. C. Haws and M. Koppe, Ehrhart Polynomials of Matroid Polytopes and Polymatroids, Discrete Comput. Geom., 42 (2009), 670-702.
- D. C. Haws, Matroids [Broken link, Oct 30 2017]
- D. C. Haws, Matroids [Copy on website of Matthias Koeppe]
- D. C. Haws, Matroids [Cached copy, pdf file only]
- Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).
Crossrefs
Cf. A294433.
Programs
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Magma
[19*n^4/8+7*n^3/4+77*n^2/8+5*n/4+1: n in [0..50]]; // Vincenzo Librandi, Sep 18 2011
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Mathematica
Table[(19*n^4 +14*n^3 +77*n^2 +10*n +1)/8, {n,0,30}] (* or *) LinearRecurrence[{5,-10,10,-5,1}, {1, 16, 94, 331, 880}, 30] (* G. C. Greubel, Apr 26 2018 *) -
PARI
x='x+O('x^30); Vec((1+11*x+24*x^2+11*x^3+10*x^4)/(1-x)^5) \\ G. C. Greubel, Apr 26 2018
Formula
G.f.: (1+11*x+24*x^2+11*x^3+10*x^4)/(1-x)^5.
a(n) = 19*n^4/8 +7*n^3/4 +77*n^2/8 +5*n/4 +1. - R. J. Mathar, Sep 11 2011
E.g.f.: (1/8)*(19*x^4 + 128*x^3 + 252*x^2 + 120*x + 1)*exp(x). - G. C. Greubel, Apr 26 2018
Comments