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A160829
Expansion of (1 + 44*x + 337*x^2 + 612*x^3 + 305*x^4 + 40*x^5 + x^6)/(1 - x)^7.
1
1, 51, 673, 4287, 17931, 57321, 152251, 353333, 740077, 1430311, 2590941, 4450051, 7310343, 11563917, 17708391, 26364361, 38294201, 54422203, 75856057, 103909671, 140127331, 186309201, 244538163, 317207997, 407052901, 517178351
OFFSET
0,2
COMMENTS
Source: the De Loera et al. article and the Haws website listed in A160747.
LINKS
J. A. De Loera, D. C. Haws and M. Koppe, Ehrhart Polynomials of Matroid Polytopes and Polymatroids, arXiv:0710.4346 [math.CO], 2007; Discrete Comput. Geom., 42 (2009), 670-702.
FORMULA
a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7), with a(0)=1, a(1)=51, a(2)=673, a(3)=4287, a(4)=17931, a(5)=57321, a(6)=152251. - Harvey P. Dale, Jun 21 2011
a(n) = (1/36)*(36 + 174*n + 391*n^2 + 513*n^3 + 442*n^4 + 213*n^5 + 67*n^6). - Harvey P. Dale, Jun 21 2011, corrected by Eric Rowland, Aug 15 2017
MAPLE
seq(coeff(series((1+44*x+337*x^2+612*x^3+305*x^4+40*x^5+x^6)/(1-x)^7, x, n+1), x, n), n=0..25); # Muniru A Asiru, Apr 29 2018
MATHEMATICA
LinearRecurrence[{7, -21, 35, -35, 21, -7, 1}, {1, 51, 673, 4287, 17931, 57321, 152251}, 30] (* or *) CoefficientList[Series[ (1+44x+337x^2+612x^3+ 305x^4+ 40x^5+x^6)/(1-x)^7, {x, 0, 30}], x] (* Harvey P. Dale, Jun 21 2011 *)
PROG
(PARI) x='x+O('x^99); Vec((1+44*x+337*x^2+612*x^3+305*x^4+40*x^5+x^6)/(1-x)^7) \\ Altug Alkan, Aug 16 2017
(Magma) [(1/36)*(36 + 174*n + 391*n^2 + 513*n^3 + 442*n^4 + 213*n^5 + 67*n^6): n in [0..30]]; // G. C. Greubel, Apr 28 2018
CROSSREFS
Sequence in context: A269622 A210055 A020278 * A160835 A231750 A232020
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Nov 18 2009
STATUS
approved