A203242 Second elementary symmetric function of the first n terms of (1, 3, 7, 15, 31, ...).

3, 31, 196, 1002, 4593, 19833, 82818, 339340, 1375639, 5543331, 22263216, 89249214, 357422541, 1430607325, 5724394990, 22901773824, 91616007699, 366482904615, 1465971463740, 5863969740370, 23456055121513, 93824589584001

Offset

2,1

Links

Robert Israel, Table of n, a(n) for n = 2..1659

Formula

Conjecture: (-103*n+258)*a(n) + (881*n-2116)*a(n-1) + 6*(-427*n+960)*a(n-2) + 4*(766*n-1545)*a(n-3) + 16*(-80*n+121)*a(n-4) = 0. - R. J. Mathar, Oct 15 2013

Empirical g.f.: -x^2*(4*x^2 + 2*x - 3)/((x - 1)^3*(2*x - 1)^2*(4*x - 1)). - Colin Barker, Aug 15 2014

From Robert Israel, Feb 01 2019: (Start)

Conjecture and empirical g.f. verified.

a(n) = 4^(n+1)/3 - (2*n+2)*2^n + (n^2+3*n)/2 + 2/3. (End)

Maple

seq(4^(n+1)/3 - (2*n+2)*2^n + (n^2+3*n)/2 + 2/3, n=2..100); # Robert Israel, Feb 01 2019

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}]  (* A203242 *)

Crossrefs

Cf. A203241.

Sequence in context: A060416 A333368 A060425 * A121099 A197746 A342260

Adjacent sequences: A203239 A203240 A203241 * A203243 A203244 A203245

Keyword

nonn,easy

Author

Clark Kimberling, Dec 31 2011

Status

approved