%I #9 Sep 08 2022 08:45:40
%S 0,0,8,384,57344,31457280,66571993088,554153860399104,
%T 18302628885633695744,2408406906263519058984960,
%U 1265174720149658640946904956928,2655859843140564331993348872396079104,22289856162789153110704890285210544923213824
%N a(n) = 2^(n^2) - 2^(n^2 - n + 1) for n >= 1; a(0) = 0.
%C Number of binary relations on an n-element set that are neither reflexive nor irreflexive. Note that "irreflexive" = "antireflexive".
%C The empty relation, unlike all others, is (trivially) both reflexive and irreflexive.
%H G. C. Greubel, <a href="/A153836/b153836.txt">Table of n, a(n) for n = 0..50</a>
%F a(n) = 2^(n^2) - 2^(n^2 -n +1) = A002416(n) - 2*A053763(n) for n >= 1; a(0) = 0.
%t Join[{0}, Table[2^(n^2) - 2^(n^2 - n + 1), {n, 1, 25}]] (* _G. C. Greubel_, Aug 30 2016 *)
%o (PARI) a(n) = if(n<=0, 0, 2^(n^2)-2^(n^2-n+1))
%o (Magma) [0] cat [2^(n^2) - 2^(n^2 -n +1): n in [1..15]]; // _Vincenzo Librandi_, Aug 31 2016
%Y Cf. A002416, A053763.
%K nonn
%O 0,3
%A _Rick L. Shepherd_, Jan 02 2009