A260340 Triangle read by rows: T(n,k) = number of sets of linear n-ads in k variables.

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 6, 1, 1, 1, 1, 22, 22, 1, 1, 1, 1, 130, 550, 130, 1, 1, 1, 1, 822, 16700, 16700, 822, 1, 1, 1, 1, 6202, 703297, 3330915, 703297, 6202, 1, 1, 1, 1, 52552, 38135272, 957659906, 957659906, 38135272, 52552, 1, 1

Offset

0,13

Comments

T(n,k) is the number of nonequivalent n X n binary matrices with k ones in every row and column up to permutation of rows. - Andrew Howroyd, Apr 18 2020

Links

Andrew Howroyd, Table of n, a(n) for n = 0..230 (rows 0..20)

P. A. MacMahon, Combinations derived from m identical sets of n different letters and their connexion with general magic squares, Proc. London Math. Soc., 17 (1917), 25-41.

Formula

T(n,k) = T(n,n-k). - Andrew Howroyd, Apr 18 2020

Example

Triangle begins:
  1;
  1, 1;
  1, 1,    1;
  1, 1,    1,      1;
  1, 1,    6,      1,       1;
  1, 1,   22,     22,       1,      1;
  1, 1,  130,    550,     130,      1,    1;
  1, 1,  822,  16700,   16700,    822,    1, 1;
  1, 1, 6202, 703297, 3330915, 703297, 6202, 1, 1;
  ...

Crossrefs

Columns k=0..4 are A000012, A000012, A002137, A333899, A333900.

Row sums are A333891.

Cf. A008300, A133687, A257463.

Sequence in context: A339747 A293901 A324891 * A040037 A344877 A356156

Adjacent sequences: A260337 A260338 A260339 * A260341 A260342 A260343

Keyword

nonn,tabl

Author

N. J. A. Sloane, Jul 30 2015

Extensions

Extended to include k=0 and more terms added by Andrew Howroyd, Apr 18 2020

Status

approved