Number of bicolored maps defined by immersions of unoriented circle into oriented sphere with n double points with edges labeled 1..2*n such that labels of successive edges along the curve (starting at any edge, going in the direction determined by the coloring) are encountered in pairs of the form {2*m-1, 2*m} (in either order).

A268560

Number of bicolored maps defined by immersions of unoriented circle into oriented sphere with n double points with edges labeled 1..2*n such that labels of successive edges along the curve (starting at any edge, going in the direction determined by the coloring) are encountered in pairs of the form {2*m-1, 2*m} (in either order).