cp's OEIS Frontend

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

%I A203242 #17 Feb 01 2019 10:55:25
%S A203242 3,31,196,1002,4593,19833,82818,339340,1375639,5543331,22263216,
%T A203242 89249214,357422541,1430607325,5724394990,22901773824,91616007699,
%U A203242 366482904615,1465971463740,5863969740370,23456055121513,93824589584001
%N A203242 Second elementary symmetric function of the first n terms of (1, 3, 7, 15, 31, ...).
%H A203242 Robert Israel, <a href="/A203242/b203242.txt">Table of n, a(n) for n = 2..1659</a>
%F A203242 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
%F A203242 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
%F A203242 From _Robert Israel_, Feb 01 2019: (Start)
%F A203242 Conjecture and empirical g.f. verified.
%F A203242 a(n) = 4^(n+1)/3 - (2*n+2)*2^n + (n^2+3*n)/2 + 2/3. (End)
%p A203242 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
%t A203242 f[k_] := 2^k - 1; t[n_] := Table[f[k], {k, 1, n}]
%t A203242 a[n_] := SymmetricPolynomial[2, t[n]]
%t A203242 Table[a[n], {n, 2, 32}]  (* A203242 *)
%Y A203242 Cf. A203241.
%K A203242 nonn,easy
%O A203242 2,1
%A A203242 _Clark Kimberling_, Dec 31 2011