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%I #32 Feb 21 2022 22:08:08
%S 1,2,16,4096,4294967296,1208925819614629174706176,
%T 6277101735386680763835789423207666416102355444464034512896
%N a(n) = 2^(n*2^(n-1)).
%C Determinant of character table of elementary Abelian group (C_2)^n.
%C a(7) has 135 digits. - _Jason Earls_, Jun 11 2001
%C Number of functions f:2^X->2^X where X is an n-element set such that f(A) is a subset of A for all A in 2^X (where 2^X denotes the power set of X). - _W. Edwin Clark_, Nov 06 2003
%H Vincenzo Librandi, <a href="/A061301/b061301.txt">Table of n, a(n) for n = 0..9</a>
%H Nate Chenette, Reed Phillips, Lara Pudwell, and Manda Riehl, <a href="https://faculty.valpo.edu/lpudwell/papers/RSEs.pdf">Occurrences of reciprocal sign epistasis in single-and multi-peaked theoretical fitness landscapes</a>, Rose-Hulman and Valparaiso Universities (2022).
%H F. Echenique, <a href="https://doi.org/10.1016/j.geb.2006.03.009">Counting Combinatorial Choice Rules</a>, Games and Economic Behavior, Vol. 58, No. 2 (2007), 231-245.
%H Lara Pudwell, Nathan Chenette, and Manda Riehl, <a href="http://faculty.valpo.edu/lpudwell/slides/JMM2020_Pudwell.pdf">Statistics on Hypercube Orientations</a>, AMS Special Session on Experimental and Computer Assisted Mathematics, Joint Mathematics Meetings (Denver 2020).
%F a(n) = 2^Sum_{i=0..n} i*binomial(n, i) = 2^(2^(n-1)*n). - _W. Edwin Clark_, Nov 06 2003
%e a(2) = 16 because the character table for C_2 X C_2 is / 1 1 1 1 / 1 -1 -1 1 / 1 -1 1 -1 / 1 1-1 -1 / with determinant 16 = (2^2)^(2^1).
%e a(1) = 2 since 2^{1} = { {}, {1}} and the functions f : 2^{1}->2^{1} satisfying f(A) is a subset of A for all A are g and h where g({})={}, g({1})={} and h({}) = {}, h({1})={1}. - _W. Edwin Clark_, Nov 06 2003
%t Table[2^(n 2^(n - 1)), {n, 0, 7}] (* _Vincenzo Librandi_, Sep 02 2018 *)
%o (Magma) [2^(n*2^(n-1)): n in [0..5]]; // _Vincenzo Librandi_, Sep 02 2018
%Y Cf. A088322.
%K nonn,easy
%O 0,2
%A Ahmed Fares (ahmedfares(AT)my-deja.com), Jun 05 2001
%E More terms from _Jason Earls_, Jun 11 2001
%E Edited by _N. J. A. Sloane_, Oct 27 2008 at the suggestion of _R. J. Mathar_
%E Offset changed to 0 by _Vincenzo Librandi_, Sep 02 2018
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