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A160829
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Expansion of (1 + 44*x + 337*x^2 + 612*x^3 + 305*x^4 + 40*x^5 + x^6)/(1 - x)^7.
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1
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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
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OFFSET
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0,2
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COMMENTS
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Source: the De Loera et al. article and the Haws website listed in A160747.
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LINKS
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FORMULA
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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
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MAPLE
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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
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MATHEMATICA
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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 *)
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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