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A080952
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Sequence associated with the recurrence a(n)=2*a(n-1)+k(k+2)a(n-2).
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2
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3, 21, 112, 504, 2016, 7392, 25344, 82368, 256256, 768768, 2236416, 6336512, 17547264, 47628288, 127008768, 333398016, 862912512, 2205220864, 5571084288, 13927710720, 34487664640, 84651540480, 206108098560, 498094571520
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OFFSET
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0,1
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COMMENTS
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The sixth column of A080928 is 2*A080952.
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LINKS
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Table of n, a(n) for n=0..23.
Index to sequences with linear recurrences with constant coefficients, signature (12,-60,160,-240,192,-64)
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FORMULA
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G.f.: (1-x)*(4*x^2-2*x+1)*(4*x^2-6*x+3)/(1-2x)^6.
a(n)=12*a(n-1)- 60*a(n-2)+160*a(n-3)-240*a(n-4)+192*a(n-5)-64*a(n-6), n>=6. [From Harvey P. Dale, June 11 2011]
Let b(n) = A000292(n+1)+n+1+A000389(n+5) = (n+1)*(n^4+14*n^3+91*n^2+254*n+360)/120 = 3, 12, 34, 80, 166, 314,.. Then a(n) = 2^n*b(n) - 2^(n-1)*b(n-1). - R. J. Mathar, Jun 11 2011
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MATHEMATICA
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LinearRecurrence[{12, -60, 160, -240, 192, -64}, {3, 21, 112, 504, 2016, 7392}, 30] (* or *) CoefficientList[Series[(1-x) (3-12x+28x^2-32x^3+ 16x^4)/ (1-2x)^6, {x, 0, 30}], x] (* From Harvey P. Dale, June 11 2011 *)
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CROSSREFS
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Sequence in context: A054147 A043012 A122120 * A183404 A121140 A005057
Adjacent sequences: A080949 A080950 A080951 * A080953 A080954 A080955
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KEYWORD
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easy,nonn
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AUTHOR
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Paul Barry, Feb 26 2003
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STATUS
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approved
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