A203244 Second elementary symmetric function of the first n terms of (1,4,16,64,256,...).

4, 84, 1428, 23188, 372372, 5963412, 95436436, 1527070356, 24433475220, 390937001620, 6254997618324, 100079984262804, 1601279837683348, 25620477760847508, 409927645605215892, 6558842335410077332, 104941477389467729556

Offset: 2

Author

Clark Kimberling, Dec 31 2011

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (21,-84,64).

Crossrefs

Cf. A006105.

Programs

Mathematica

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 *)

PARI

Vec(-4*x^2/((x-1)*(4*x-1)*(16*x-1)) + O(x^100)) \\ Colin Barker, Aug 15 2014

Formula

a(n) = 4*A006105(n).

From Colin Barker, Aug 15 2014: (Start)

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)

Extensions

Typo in formula fixed by Colin Barker, Aug 15 2014