Number of partitions of [n] having exactly one parity change within the partition.

Terms

a(0) =0a(1) =0a(2) =2a(3) =1a(4) =3a(5) =2a(6) =7a(7) =5a(8) =20a(9) =15a(10) =67a(11) =52a(12) =255a(13) =203a(14) =1080a(15) =877a(16) =5017a(17) =4140a(18) =25287a(19) =21147a(20) =137122a(21) =115975a(22) =794545a(23) =678570a(24) =4892167a(25) =4213597a(26) =31858034a(27) =27644437a(28) =218543759a(29) =190899322