A203241 Second elementary symmetric function of the first n terms of (1,2,4,8,...).

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

Author

Clark Kimberling, Dec 31 2011

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (7,-14,8).

Crossrefs

Cf. A006095.

Programs

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 *)

PARI

Vec(-2*x^2 / ((x-1)*(2*x-1)*(4*x-1)) + O(x^100)) \\ Colin Barker, Aug 15 2014

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