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

0,2

Comments

Source: the De Loera et al. article and the Haws website.

The coefficient of x^4 should be 1 rather than 10, and so this is an erroneous version of A294433. However, it remains in the OEIS in accordance with our policy of including published but erroneous sequences, to serve as pointers to the correct versions. - N. J. A. Sloane, Oct 30 2017

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/a> [Cached copy, pdf file only]

Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

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

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 *)

Prog

(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
(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

Crossrefs

Cf. A294433.

Sequence in context: A305639 A317033 A294433 * A305908 A316880 A317150

Adjacent sequences: A160747 A160748 A160749 * A160751 A160752 A160753

Keyword

nonn,easy

Author

N. J. A. Sloane, Nov 18 2009

Status

approved