A140786 Number of n X n symmetric binary matrices with no more than one greater count of 1s than 0s in and to the left of any position.

1, 2, 5, 30, 230, 4600, 118735, 8311450, 756803538, 190714491576, 62835570762274, 58060067384341176, 70381397432713019444, 241548955989071082731808, 1090217292455289464608212443, 14031096553899575409507694141410