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A325912 a(n) = (-1)^n * Sum_{k=0..n} (-1)^k*2^(2^k).

%I A325912 #28 Sep 29 2024 11:56:13
%S A325912 2,2,14,242,65294,4294902002,18446744069414649614,
%T A325912 340282366920938463444927863362353561842,
%U A325912 115792089237316195423570985008687907852929702298719625576012656144550776078094
%N A325912 a(n) = (-1)^n * Sum_{k=0..n} (-1)^k*2^(2^k).
%H A325912 Seiichi Manyama, <a href="/A325912/b325912.txt">Table of n, a(n) for n = 0..11</a>
%H A325912 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 A325912 a(n) = A001146(n) - a(n-1).
%e A325912 a(0) = 2^1 = 2.
%e A325912 a(1) = 2^2  - 2^1 = 2.
%e A325912 a(2) = 2^4  - 2^2 + 2^1 = 14.
%e A325912 a(3) = 2^8  - 2^4 + 2^2 - 2^1 = 242.
%e A325912 a(4) = 2^16 - 2^8 + 2^4 - 2^2 + 2^1 = 65294.
%t A325912 a[n_] := (-1)^n * Sum[(-1)^k * 2^(2^k), {k, 0, n}]; Array[a, 9, 0] (* _Amiram Eldar_, May 07 2021 *)
%o A325912 (PARI) {a(n) = (-1)^n*sum(k=0,n,(-1)^k*2^2^k)}
%Y A325912 Cf. A001146, A060803, A325910.
%K A325912 nonn
%O A325912 0,1
%A A325912 _Seiichi Manyama_, Sep 08 2019