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%I #7 Jun 21 2019 22:45:42
%S 1,2,65,986410,56874039553217,42163840398198058854693626,
%T 1011182700521015817607065606491025592595137,
%U 1653481537585545171449931620186035466059689728986775126016505970
%N Number of sequences of distinct ordered pairs of positive integers up to n.
%F a(n) = A000522(n^2).
%e The a(2) = 65 sequences:
%e () (11) (11,12) (11,12,21) (11,12,21,22)
%e (12) (11,21) (11,12,22) (11,12,22,21)
%e (21) (11,22) (11,21,12) (11,21,12,22)
%e (22) (12,11) (11,21,22) (11,21,22,12)
%e (12,21) (11,22,12) (11,22,12,21)
%e (12,22) (11,22,21) (11,22,21,12)
%e (21,11) (12,11,21) (12,11,21,22)
%e (21,12) (12,11,22) (12,11,22,21)
%e (21,22) (12,21,11) (12,21,11,22)
%e (22,11) (12,21,22) (12,21,22,11)
%e (22,12) (12,22,11) (12,22,11,21)
%e (22,21) (12,22,21) (12,22,21,11)
%e (21,11,12) (21,11,12,22)
%e (21,11,22) (21,11,22,12)
%e (21,12,11) (21,12,11,22)
%e (21,12,22) (21,12,22,11)
%e (21,22,11) (21,22,11,12)
%e (21,22,12) (21,22,12,11)
%e (22,11,12) (22,11,12,21)
%e (22,11,21) (22,11,21,12)
%e (22,12,11) (22,12,11,21)
%e (22,12,21) (22,12,21,11)
%e (22,21,11) (22,21,11,12)
%e (22,21,12) (22,21,12,11)
%t Table[Sum[k!*Binomial[n^2,k],{k,0,n^2}],{n,0,4}]
%Y Cf. A000522, A000595, A002416, A095661, A229865, A326209, A326237, A326251, A326252, A326258.
%K nonn
%O 0,2
%A _Gus Wiseman_, Jun 21 2019