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A203241
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Second elementary symmetric function of the first n terms of (1,2,4,8,...).
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4
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2, 14, 70, 310, 1302, 5334, 21590, 86870, 348502, 1396054, 5588310, 22361430, 89462102, 357881174, 1431590230, 5726491990, 22906230102, 91625444694, 366502827350, 1466013406550, 5864057820502, 23456239670614, 93824975459670
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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) = (2 - 3*2^n + 4^n)/3.
a(n) = 7*a(n-1) - 14*a(n-2) + 8*a(n-3).
G.f.: -2*x^2 / ((x-1)*(2*x-1)*(4*x-1)). (End)
a(n) = Sum_{k=0...n-2} 2^k*(2^(n-1)-1+2^k). - J. M. Bergot, Mar 21 2018
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MATHEMATICA
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f[k_] := 2^(k - 1); t[n_] := Table[f[k], {k, 1, n}]
a[n_] := SymmetricPolynomial[2, t[n]]
Table[a[n], {n, 2, 32}] (* A203241 *)
Table[a[n]/2, {n, 2, 32}] (* A006095 *)
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PROG
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(PARI) Vec(-2*x^2 / ((x-1)*(2*x-1)*(4*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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STATUS
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approved
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