A333165 Number of non-isomorphic 2n X 2n symmetric matrices with entries in {+1, -1} and all rows and columns summing to zero.

1, 1, 2, 5, 66, 7937, 10211144, 133506398361, 18551599312980440, 28652629505982770906471, 510824181488832447063505273252

Offset: 0

Author

Andrew Howroyd, Mar 11 2020

Keywords

• nonn
• more

Comments

a(n) is the number of non-isomorphic 2n X 2n symmetric binary matrices with n ones in every row and column.

Examples

			The a(1) = 1 matrix is:
  [+ -]
  [- +]
The a(2) = 2 matrices are:
  [+ + - -]   [+ + - -]
  [+ + - -]   [+ - + -]
  [- - + +]   [- + - +]
  [- - + +]   [- - + +]
		

Crossrefs

Central coefficients of A333159.

Cf. A333164, A333166.

Formula

a(n) = A333159(2*n, n).