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A189375
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Expansion of 1/((1-x)^5*(x^3+x^2+x+1)^3).
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4
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1, 2, 3, 4, 8, 12, 16, 20, 30, 40, 50, 60, 80, 100, 120, 140, 175, 210, 245, 280, 336, 392, 448, 504, 588, 672, 756, 840, 960, 1080, 1200, 1320, 1485, 1650, 1815, 1980, 2200, 2420, 2640, 2860, 3146, 3432, 3718, 4004, 4368
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OFFSET
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0,2
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COMMENTS
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The Gi1 triangle sums of A139600 lead to the sequence given above, see the formulas. For the definitions of the Gi1 and other triangle sums see A180662.
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (2, -1, 0, 3, -6, 3, 0, -3, 6, -3, 0, 1, -2, 1).
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FORMULA
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a(n) = (2*n^4+56*n^3+538*n^2+2044*n+2469+3*((2*n^2+28*n+89)*(-1)^n+(4*(-1)^((2*n-1+(-1)^n)/4)*(n^2+16*n+57-(n^2+12*n+29)*(-1)^n))))/3072. - Luce ETIENNE, Jun 25 2015
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MAPLE
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a:= n-> coeff(series(1/((1-x)^5*(x^3+x^2+x+1)^3), x, n+1), x, n):
seq(a(n), n=0..50);
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MATHEMATICA
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CoefficientList[Series[1/((1-x)^5(x^3+x^2+x+1)^3), {x, 0, 50}], x] (* or *) LinearRecurrence[{2, -1, 0, 3, -6, 3, 0, -3, 6, -3, 0, 1, -2, 1}, {1, 2, 3, 4, 8, 12, 16, 20, 30, 40, 50, 60, 80, 100}, 50] (* Harvey P. Dale, Dec 05 2014 *)
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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