Number of noncrossing partitions of [n] that contain exactly one singleton.

Terms

a(0) =0a(1) =1a(2) =0a(3) =3a(4) =4a(5) =15a(6) =36a(7) =105a(8) =288a(9) =819a(10) =2320a(11) =6633a(12) =19020a(13) =54769a(14) =158172a(15) =458055a(16) =1329552a(17) =3867075a(18) =11267856a(19) =32884953a(20) =96111900a(21) =281267469a(22) =824083260a(23) =2417052267a(24) =7096175856a(25) =20852160525a(26) =61324675776a(27) =180488550375a(28) =531581605828