A326253 Number of sequences of distinct ordered pairs of positive integers up to n.

1, 2, 65, 986410, 56874039553217, 42163840398198058854693626, 1011182700521015817607065606491025592595137, 1653481537585545171449931620186035466059689728986775126016505970

Offset

0,2

Links

Table of n, a(n) for n=0..7.

Formula

a(n) = A000522(n^2).

Example

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)

Mathematica

Table[Sum[k!*Binomial[n^2, k], {k, 0, n^2}], {n, 0, 4}]

Crossrefs

Cf. A000522, A000595, A002416, A095661, A229865, A326209, A326237, A326251, A326252, A326258.

Sequence in context: A228081 A214366 A220596 * A003821 A055765 A265996

Adjacent sequences: A326250 A326251 A326252 * A326254 A326255 A326256

Keyword

nonn

Author

Gus Wiseman, Jun 21 2019

Status

approved