A181174 The "Row2" sums of the powers-of-2 triangle A000079.

1, 2, 24, 320, 11264, 688128, 90177536, 22817013760, 11751030521856, 11997870882291712, 24607668363952390144, 100719222642454151823360, 825394103341888069030641664, 13520781109074923362448234774528

Offset: 0

Author

Johannes W. Meijer, Oct 10 2010

Keywords

• easy
• nonn

Comments

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.

Programs

Mathematica

f[k_] := (2^k) (-1)^(k + 1)
t[n_] := Table[f[k], {k, 1, n}]
a[n_] := SymmetricPolynomial[n - 1, t[n]]
Table[a[n], {n, 1, 22}]    (* A181174 signed *)
(* Clark Kimberling, Dec 30 2011 *)

Formula

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

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