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a(n) = (-1)^n * Sum_{k=0..n} (-1)^k*2^(2^k).
2

%I #28 Sep 29 2024 11:56:13

%S 2,2,14,242,65294,4294902002,18446744069414649614,

%T 340282366920938463444927863362353561842,

%U 115792089237316195423570985008687907852929702298719625576012656144550776078094

%N a(n) = (-1)^n * Sum_{k=0..n} (-1)^k*2^(2^k).

%H Seiichi Manyama, <a href="/A325912/b325912.txt">Table of n, a(n) for n = 0..11</a>

%H Sylvia Wenmackers, <a href="https://doi.org/10.36253/jpm-2939">On the Limits of Comparing Subset Sizes within N</a>, J. Phil. Math. (2024) Vol. 1, 223-251. See p. 229.

%F a(n) = A001146(n) - a(n-1).

%e a(0) = 2^1 = 2.

%e a(1) = 2^2 - 2^1 = 2.

%e a(2) = 2^4 - 2^2 + 2^1 = 14.

%e a(3) = 2^8 - 2^4 + 2^2 - 2^1 = 242.

%e a(4) = 2^16 - 2^8 + 2^4 - 2^2 + 2^1 = 65294.

%t a[n_] := (-1)^n * Sum[(-1)^k * 2^(2^k), {k, 0, n}]; Array[a, 9, 0] (* _Amiram Eldar_, May 07 2021 *)

%o (PARI) {a(n) = (-1)^n*sum(k=0,n,(-1)^k*2^2^k)}

%Y Cf. A001146, A060803, A325910.

%K nonn

%O 0,1

%A _Seiichi Manyama_, Sep 08 2019