A326253 Number of sequences of distinct ordered pairs of positive integers up to n.
1, 2, 65, 986410, 56874039553217, 42163840398198058854693626, 1011182700521015817607065606491025592595137, 1653481537585545171449931620186035466059689728986775126016505970
Offset: 0
Keywords
Examples
The a(2) = 65 sequences:
() (11) (11,12) (11,12,21) (11,12,21,22)
(12) (11,21) (11,12,22) (11,12,22,21)
(21) (11,22) (11,21,12) (11,21,12,22)
(22) (12,11) (11,21,22) (11,21,22,12)
(12,21) (11,22,12) (11,22,12,21)
(12,22) (11,22,21) (11,22,21,12)
(21,11) (12,11,21) (12,11,21,22)
(21,12) (12,11,22) (12,11,22,21)
(21,22) (12,21,11) (12,21,11,22)
(22,11) (12,21,22) (12,21,22,11)
(22,12) (12,22,11) (12,22,11,21)
(22,21) (12,22,21) (12,22,21,11)
(21,11,12) (21,11,12,22)
(21,11,22) (21,11,22,12)
(21,12,11) (21,12,11,22)
(21,12,22) (21,12,22,11)
(21,22,11) (21,22,11,12)
(21,22,12) (21,22,12,11)
(22,11,12) (22,11,12,21)
(22,11,21) (22,11,21,12)
(22,12,11) (22,12,11,21)
(22,12,21) (22,12,21,11)
(22,21,11) (22,21,11,12)
(22,21,12) (22,21,12,11)
Crossrefs
Programs
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Mathematica
Table[Sum[k!*Binomial[n^2,k],{k,0,n^2}],{n,0,4}]
Formula
a(n) = A000522(n^2).