A333164 Number of 2n X 2n symmetric matrices with entries in {+1, -1} and all rows and columns summing to zero.

1, 2, 18, 1760, 1944530, 26615510712, 4762109992158288, 11528251571501588791296, 386860001875783390762182911250, 183238648400953515891207813311894423000, 1242327573587456839123512395835593196519781229768, 121917941188016997420391711911475819481799846311888884541952

Offset

0,2

Comments

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

Links

Table of n, a(n) for n=0..11.

Formula

a(n) = A333157(2*n, n).

a(n) = A213793(2*n). - Andrew Howroyd, Apr 08 2020

Example

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

Crossrefs

Central coefficients of A333157.

Cf. A213793, A333165, A333166.

Sequence in context: A155206 A334623 A260610 * A076954 A206847 A259654

Adjacent sequences: A333161 A333162 A333163 * A333165 A333166 A333167

Keyword

nonn

Author

Andrew Howroyd, Mar 11 2020

Status

approved