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A203241
Second elementary symmetric function of the first n terms of (1,2,4,8,...).
4
2, 14, 70, 310, 1302, 5334, 21590, 86870, 348502, 1396054, 5588310, 22361430, 89462102, 357881174, 1431590230, 5726491990, 22906230102, 91625444694, 366502827350, 1466013406550, 5864057820502, 23456239670614, 93824975459670
OFFSET
2,1
FORMULA
a(n) = 2*A006095(n).
From Colin Barker, Aug 15 2014: (Start)
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
MATHEMATICA
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 *)
PROG
(PARI) Vec(-2*x^2 / ((x-1)*(2*x-1)*(4*x-1)) + O(x^100)) \\ Colin Barker, Aug 15 2014
CROSSREFS
Cf. A006095.
Sequence in context: A375874 A258138 A206947 * A072888 A171012 A094583
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Dec 31 2011
STATUS
approved