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A081909
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a(n) = 3^n(n^2 - n + 18)/18.
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4
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1, 3, 10, 36, 135, 513, 1944, 7290, 26973, 98415, 354294, 1259712, 4428675, 15411789, 53144100, 181752822, 617003001, 2080591515, 6973568802, 23245229340, 77096677311, 254535261273, 836828256240, 2740612539186
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OFFSET
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0,2
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COMMENTS
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Binomial transform of A081908. 3rd binomial transform of (1,0,1,0,0,0,...). Case k=3 where a(n,k) = k^n*(n^2 - n + 2k^2)/(2k^2) with g.f. (1 - 2kx + (k^2+1)x^2)/(1-kx)^3.
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LINKS
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FORMULA
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a(n) = 3^n*(n^2 - n + 18)/18.
G.f.: (1 - 6x + 10x^2)/(1-3x)^3.
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MATHEMATICA
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Table[3^n(n^2-n+18)/18, {n, 0, 30}] (* or *) CoefficientList[Series[ (1-6x+10x^2)/(1-3x)^3, {x, 0, 30}], x] (* Harvey P. Dale, Apr 26 2011 *)
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PROG
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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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