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The "Row2" sums of the powers-of-2 triangle A000079
3

%I #6 Aug 03 2014 14:27:19

%S 1,2,24,320,11264,688128,90177536,22817013760,11751030521856,

%T 11997870882291712,24607668363952390144,100719222642454151823360,

%U 825394103341888069030641664,13520781109074923362448234774528

%N The "Row2" sums of the powers-of-2 triangle A000079

%C The a(n) represent the "Row2" sums, see A180662, of the powers-of-2 triangle A000079. This sequence is related to the Jacobsthal and triangular numbers.

%F a(n) = 2^(n*(n+1)/2)*(2^(n+1)+(-1)^n)/3.

%F a(n) = A001045(n+1)*2^A000217(n).

%t f[k_] := (2^k) (-1)^(k + 1)

%t t[n_] := Table[f[k], {k, 1, n}]

%t a[n_] := SymmetricPolynomial[n - 1, t[n]]

%t Table[a[n], {n, 1, 22}] (* A181174 signed *)

%t (* _Clark Kimberling_, Dec 30 2011 *)

%K easy,nonn

%O 0,2

%A _Johannes W. Meijer_, Oct 10 2010