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A203244
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Second elementary symmetric function of the first n terms of (1,4,16,64,256,...).
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1
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4, 84, 1428, 23188, 372372, 5963412, 95436436, 1527070356, 24433475220, 390937001620, 6254997618324, 100079984262804, 1601279837683348, 25620477760847508, 409927645605215892, 6558842335410077332, 104941477389467729556
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OFFSET
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2,1
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LINKS
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FORMULA
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a(n) = (4-5*4^n+16^n)/45.
a(n) = 21*a(n-1)-84*a(n-2)+64*a(n-3).
G.f.: -4*x^2 / ((x-1)*(4*x-1)*(16*x-1)). (End)
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MATHEMATICA
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f[k_] := 4^(k - 1); t[n_] := Table[f[k], {k, 1, n}]
a[n_] := SymmetricPolynomial[2, t[n]]
Table[a[n], {n, 2, 32}] (* A203244 *)
Table[a[n]/4, {n, 2, 32}] (* A006105 *)
LinearRecurrence[{21, -84, 64}, {4, 84, 1428}, 20] (* Harvey P. Dale, Aug 12 2015 *)
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PROG
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(PARI) Vec(-4*x^2/((x-1)*(4*x-1)*(16*x-1)) + O(x^100)) \\ Colin Barker, Aug 15 2014
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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