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Number of nonisomorphic unordered pairs of derangements of an n-set.
3

%I #6 May 03 2023 21:36:58

%S 1,0,1,2,7,16,84,403,3028,25431,250377,2726361,32622807,423310642,

%T 5921052187,88759485250,1419511438134,24123164524402,434094104795638,

%U 8245872981392311,164885609163058430,3462034812141768953,76154237902292661820,1751339843001023621169

%N Number of nonisomorphic unordered pairs of derangements of an n-set.

%C Isomorphism is up to permutation of the elements of the n-set.

%H Andrew Howroyd, <a href="/A362760/b362760.txt">Table of n, a(n) for n = 0..50</a>

%e The a(3)=2 nonisomorphic pairs of derangements with permutations shown in cycle notation are:

%e {(123), (123)},

%e {(123), (132)}.

%e The a(4)=7 nonisomorphic pairs of derangements are:

%e {(12)(34), (12)(34)},

%e {(12)(34), (13)(24)},

%e {(12)(34), (1234)},

%e {(12)(34), (1324)},

%e {(1234), (1234)},

%e {(1234), (1243)},

%e {(1234), (1432)}.

%Y Column k=2 of A362759.

%Y Cf. A000166 (derangements), A362645.

%K nonn

%O 0,4

%A _Andrew Howroyd_, May 02 2023