Number of labeled n-vertex 2-edge multigraphs that are neither crossing nor nesting.

Terms

a(0) =0a(1) =0a(2) =1a(3) =9a(4) =32a(5) =80a(6) =165a(7) =301a(8) =504a(9) =792a(10) =1185a(11) =1705a(12) =2376a(13) =3224a(14) =4277a(15) =5565a(16) =7120a(17) =8976a(18) =11169a(19) =13737a(20) =16720a(21) =20160a(22) =24101a(23) =28589a(24) =33672a(25) =39400a(26) =45825a(27) =53001a(28) =60984a(29) =69832